位相空間の例 - 機械学習基礎理論独習

はじめに

「集合・位相入門」という本を読んでいるのですが、p153に
「 $S$ が $3$ つの元から成る集合 $S=\{p,q,r\}$ である場合には、 $S$ における位相をを全部書き上げることは
もはやそれほど容易ではない。しかし、注意深く検討すれば、この集合における位相は全部で $29$ 個あることがわかる。
(実際に $29$ 個の位相を書き上げることは読者の練習問題とする)」
とあり、気になったので、プログラムを組んで確認してみました。
プログラムはこちらで動かすことができます。

以下、プログラムで出力したものを貼り付けます。

$S=\{p\}$ の場合

$S$ における位相は $1$ つです。

$\begin{eqnarray} &&\mathfrak{O}=\{\varnothing,S\}\\ \end{eqnarray}$

$S=\{p,q\}$ の場合

$S$ における位相は $4$ つです。

$S=\{p,q,r\}$ の場合

$S$ における位相は $29$ つです。

$\begin{eqnarray} &&\mathfrak{O}_{1}=\{\varnothing,S\}\\ &&\mathfrak{O}_{2}=\{\varnothing,\{p\},S\}\\ &&\mathfrak{O}_{3}=\{\varnothing,\{q\},S\}\\ &&\mathfrak{O}_{4}=\{\varnothing,\{r\},S\}\\ &&\mathfrak{O}_{5}=\{\varnothing,\{p,q\},S\}\\ &&\mathfrak{O}_{6}=\{\varnothing,\{p,r\},S\}\\ &&\mathfrak{O}_{7}=\{\varnothing,\{q,r\},S\}\\ &&\mathfrak{O}_{8}=\{\varnothing,\{p\},\{p,q\},S\}\\ &&\mathfrak{O}_{9}=\{\varnothing,\{p\},\{p,r\},S\}\\ &&\mathfrak{O}_{10}=\{\varnothing,\{p\},\{q,r\},S\}\\ &&\mathfrak{O}_{11}=\{\varnothing,\{q\},\{p,q\},S\}\\ &&\mathfrak{O}_{12}=\{\varnothing,\{q\},\{p,r\},S\}\\ &&\mathfrak{O}_{13}=\{\varnothing,\{q\},\{q,r\},S\}\\ &&\mathfrak{O}_{14}=\{\varnothing,\{r\},\{p,q\},S\}\\ &&\mathfrak{O}_{15}=\{\varnothing,\{r\},\{p,r\},S\}\\ &&\mathfrak{O}_{16}=\{\varnothing,\{r\},\{q,r\},S\}\\ &&\mathfrak{O}_{17}=\{\varnothing,\{p\},\{q\},\{p,q\},S\}\\ &&\mathfrak{O}_{18}=\{\varnothing,\{p\},\{r\},\{p,r\},S\}\\ &&\mathfrak{O}_{19}=\{\varnothing,\{p\},\{p,q\},\{p,r\},S\}\\ &&\mathfrak{O}_{20}=\{\varnothing,\{q\},\{r\},\{q,r\},S\}\\ &&\mathfrak{O}_{21}=\{\varnothing,\{q\},\{p,q\},\{q,r\},S\}\\ &&\mathfrak{O}_{22}=\{\varnothing,\{r\},\{p,r\},\{q,r\},S\}\\ &&\mathfrak{O}_{23}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r\},S\}\\ &&\mathfrak{O}_{24}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,r\},S\}\\ &&\mathfrak{O}_{25}=\{\varnothing,\{p\},\{r\},\{p,q\},\{p,r\},S\}\\ &&\mathfrak{O}_{26}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,r\},S\}\\ &&\mathfrak{O}_{27}=\{\varnothing,\{q\},\{r\},\{p,q\},\{q,r\},S\}\\ &&\mathfrak{O}_{28}=\{\varnothing,\{q\},\{r\},\{p,r\},\{q,r\},S\}\\ &&\mathfrak{O}_{29}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},S\}\\ \end{eqnarray}$

$S=\{p,q,r,s\}$ の場合

$S$ における位相は $355$ つ(多分)です。(数式をまとめて貼り付けると、エラーが出るので分けて表示しています。)

$\begin{eqnarray} &&\mathfrak{O}_{1}=\{\varnothing,S\}\\ &&\mathfrak{O}_{2}=\{\varnothing,\{p\},S\}\\ &&\mathfrak{O}_{3}=\{\varnothing,\{q\},S\}\\ &&\mathfrak{O}_{4}=\{\varnothing,\{r\},S\}\\ &&\mathfrak{O}_{5}=\{\varnothing,\{s\},S\}\\ &&\mathfrak{O}_{6}=\{\varnothing,\{p,q\},S\}\\ &&\mathfrak{O}_{7}=\{\varnothing,\{p,r\},S\}\\ &&\mathfrak{O}_{8}=\{\varnothing,\{p,s\},S\}\\ &&\mathfrak{O}_{9}=\{\varnothing,\{q,r\},S\}\\ &&\mathfrak{O}_{10}=\{\varnothing,\{q,s\},S\}\\ &&\mathfrak{O}_{11}=\{\varnothing,\{r,s\},S\}\\ &&\mathfrak{O}_{12}=\{\varnothing,\{p,q,r\},S\}\\ &&\mathfrak{O}_{13}=\{\varnothing,\{p,q,s\},S\}\\ &&\mathfrak{O}_{14}=\{\varnothing,\{p,r,s\},S\}\\ &&\mathfrak{O}_{15}=\{\varnothing,\{q,r,s\},S\}\\ &&\mathfrak{O}_{16}=\{\varnothing,\{p\},\{p,q\},S\}\\ &&\mathfrak{O}_{17}=\{\varnothing,\{p\},\{p,r\},S\}\\ &&\mathfrak{O}_{18}=\{\varnothing,\{p\},\{p,s\},S\}\\ &&\mathfrak{O}_{19}=\{\varnothing,\{p\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{20}=\{\varnothing,\{p\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{21}=\{\varnothing,\{p\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{22}=\{\varnothing,\{p\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{23}=\{\varnothing,\{q\},\{p,q\},S\}\\ &&\mathfrak{O}_{24}=\{\varnothing,\{q\},\{q,r\},S\}\\ &&\mathfrak{O}_{25}=\{\varnothing,\{q\},\{q,s\},S\}\\ &&\mathfrak{O}_{26}=\{\varnothing,\{q\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{27}=\{\varnothing,\{q\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{28}=\{\varnothing,\{q\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{29}=\{\varnothing,\{q\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{30}=\{\varnothing,\{r\},\{p,r\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{31}=\{\varnothing,\{r\},\{q,r\},S\}\\ &&\mathfrak{O}_{32}=\{\varnothing,\{r\},\{r,s\},S\}\\ &&\mathfrak{O}_{33}=\{\varnothing,\{r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{34}=\{\varnothing,\{r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{35}=\{\varnothing,\{r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{36}=\{\varnothing,\{r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{37}=\{\varnothing,\{s\},\{p,s\},S\}\\ &&\mathfrak{O}_{38}=\{\varnothing,\{s\},\{q,s\},S\}\\ &&\mathfrak{O}_{39}=\{\varnothing,\{s\},\{r,s\},S\}\\ &&\mathfrak{O}_{40}=\{\varnothing,\{s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{41}=\{\varnothing,\{s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{42}=\{\varnothing,\{s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{43}=\{\varnothing,\{s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{44}=\{\varnothing,\{p,q\},\{r,s\},S\}\\ &&\mathfrak{O}_{45}=\{\varnothing,\{p,q\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{46}=\{\varnothing,\{p,q\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{47}=\{\varnothing,\{p,r\},\{q,s\},S\}\\ &&\mathfrak{O}_{48}=\{\varnothing,\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{49}=\{\varnothing,\{p,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{50}=\{\varnothing,\{p,s\},\{q,r\},S\}\\ &&\mathfrak{O}_{51}=\{\varnothing,\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{52}=\{\varnothing,\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{53}=\{\varnothing,\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{54}=\{\varnothing,\{q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{55}=\{\varnothing,\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{56}=\{\varnothing,\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{57}=\{\varnothing,\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{58}=\{\varnothing,\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{59}=\{\varnothing,\{p\},\{q\},\{p,q\},S\}\\ &&\mathfrak{O}_{60}=\{\varnothing,\{p\},\{r\},\{p,r\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{61}=\{\varnothing,\{p\},\{s\},\{p,s\},S\}\\ &&\mathfrak{O}_{62}=\{\varnothing,\{p\},\{p,q\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{63}=\{\varnothing,\{p\},\{p,q\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{64}=\{\varnothing,\{p\},\{p,q\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{65}=\{\varnothing,\{p\},\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{66}=\{\varnothing,\{p\},\{p,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{67}=\{\varnothing,\{p\},\{p,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{68}=\{\varnothing,\{p\},\{p,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{69}=\{\varnothing,\{p\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{70}=\{\varnothing,\{p\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{71}=\{\varnothing,\{p\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{72}=\{\varnothing,\{p\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{73}=\{\varnothing,\{p\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{74}=\{\varnothing,\{q\},\{r\},\{q,r\},S\}\\ &&\mathfrak{O}_{75}=\{\varnothing,\{q\},\{s\},\{q,s\},S\}\\ &&\mathfrak{O}_{76}=\{\varnothing,\{q\},\{p,q\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{77}=\{\varnothing,\{q\},\{p,q\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{78}=\{\varnothing,\{q\},\{p,q\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{79}=\{\varnothing,\{q\},\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{80}=\{\varnothing,\{q\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{81}=\{\varnothing,\{q\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{82}=\{\varnothing,\{q\},\{q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{83}=\{\varnothing,\{q\},\{q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{84}=\{\varnothing,\{q\},\{q,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{85}=\{\varnothing,\{q\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{86}=\{\varnothing,\{q\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{87}=\{\varnothing,\{q\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{88}=\{\varnothing,\{r\},\{s\},\{r,s\},S\}\\ &&\mathfrak{O}_{89}=\{\varnothing,\{r\},\{p,q\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{90}=\{\varnothing,\{r\},\{p,r\},\{p,q,r\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{91}=\{\varnothing,\{r\},\{p,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{92}=\{\varnothing,\{r\},\{p,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{93}=\{\varnothing,\{r\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{94}=\{\varnothing,\{r\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{95}=\{\varnothing,\{r\},\{q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{96}=\{\varnothing,\{r\},\{q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{97}=\{\varnothing,\{r\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{98}=\{\varnothing,\{r\},\{r,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{99}=\{\varnothing,\{r\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{100}=\{\varnothing,\{r\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{101}=\{\varnothing,\{s\},\{p,q\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{102}=\{\varnothing,\{s\},\{p,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{103}=\{\varnothing,\{s\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{104}=\{\varnothing,\{s\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{105}=\{\varnothing,\{s\},\{p,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{106}=\{\varnothing,\{s\},\{q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{107}=\{\varnothing,\{s\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{108}=\{\varnothing,\{s\},\{q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{109}=\{\varnothing,\{s\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{110}=\{\varnothing,\{s\},\{r,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{111}=\{\varnothing,\{s\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{112}=\{\varnothing,\{s\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{113}=\{\varnothing,\{p,q\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{114}=\{\varnothing,\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{115}=\{\varnothing,\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{116}=\{\varnothing,\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{117}=\{\varnothing,\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{118}=\{\varnothing,\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{119}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{120}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,q,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{121}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{122}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{123}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{124}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{125}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{126}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{127}=\{\varnothing,\{p\},\{s\},\{p,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{128}=\{\varnothing,\{p\},\{s\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{129}=\{\varnothing,\{p\},\{s\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{130}=\{\varnothing,\{p\},\{s\},\{p,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{131}=\{\varnothing,\{p\},\{p,q\},\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{132}=\{\varnothing,\{p\},\{p,q\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{133}=\{\varnothing,\{p\},\{p,q\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{134}=\{\varnothing,\{p\},\{p,q\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{135}=\{\varnothing,\{p\},\{p,r\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{136}=\{\varnothing,\{p\},\{p,r\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{137}=\{\varnothing,\{p\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{138}=\{\varnothing,\{p\},\{p,s\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{139}=\{\varnothing,\{p\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{140}=\{\varnothing,\{p\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{141}=\{\varnothing,\{p\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{142}=\{\varnothing,\{p\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{143}=\{\varnothing,\{q\},\{r\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{144}=\{\varnothing,\{q\},\{r\},\{q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{145}=\{\varnothing,\{q\},\{r\},\{q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{146}=\{\varnothing,\{q\},\{r\},\{q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{147}=\{\varnothing,\{q\},\{s\},\{q,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{148}=\{\varnothing,\{q\},\{s\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{149}=\{\varnothing,\{q\},\{s\},\{q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{150}=\{\varnothing,\{q\},\{s\},\{q,s\},\{q,r,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{151}=\{\varnothing,\{q\},\{p,q\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{152}=\{\varnothing,\{q\},\{p,q\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{153}=\{\varnothing,\{q\},\{p,q\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{154}=\{\varnothing,\{q\},\{p,q\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{155}=\{\varnothing,\{q\},\{p,r\},\{q,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{156}=\{\varnothing,\{q\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{157}=\{\varnothing,\{q\},\{p,s\},\{q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{158}=\{\varnothing,\{q\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{159}=\{\varnothing,\{q\},\{q,r\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{160}=\{\varnothing,\{q\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{161}=\{\varnothing,\{q\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{162}=\{\varnothing,\{q\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{163}=\{\varnothing,\{r\},\{s\},\{r,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{164}=\{\varnothing,\{r\},\{s\},\{r,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{165}=\{\varnothing,\{r\},\{s\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{166}=\{\varnothing,\{r\},\{s\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{167}=\{\varnothing,\{r\},\{p,q\},\{r,s\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{168}=\{\varnothing,\{r\},\{p,q\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{169}=\{\varnothing,\{r\},\{p,r\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{170}=\{\varnothing,\{r\},\{p,r\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{171}=\{\varnothing,\{r\},\{p,r\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{172}=\{\varnothing,\{r\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{173}=\{\varnothing,\{r\},\{p,s\},\{q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{174}=\{\varnothing,\{r\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{175}=\{\varnothing,\{r\},\{q,r\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{176}=\{\varnothing,\{r\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{177}=\{\varnothing,\{r\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{178}=\{\varnothing,\{r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{179}=\{\varnothing,\{s\},\{p,q\},\{r,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{180}=\{\varnothing,\{s\},\{p,q\},\{p,q,r\},\{p,q,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{181}=\{\varnothing,\{s\},\{p,r\},\{q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{182}=\{\varnothing,\{s\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{183}=\{\varnothing,\{s\},\{p,s\},\{q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{184}=\{\varnothing,\{s\},\{p,s\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{185}=\{\varnothing,\{s\},\{p,s\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{186}=\{\varnothing,\{s\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{187}=\{\varnothing,\{s\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{188}=\{\varnothing,\{s\},\{q,s\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{189}=\{\varnothing,\{s\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{190}=\{\varnothing,\{s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{191}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{192}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{193}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{194}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{195}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{196}=\{\varnothing,\{p\},\{r\},\{p,q\},\{p,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{197}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{198}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{199}=\{\varnothing,\{p\},\{r\},\{p,r\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{200}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{201}=\{\varnothing,\{p\},\{s\},\{p,q\},\{p,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{202}=\{\varnothing,\{p\},\{s\},\{p,r\},\{p,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{203}=\{\varnothing,\{p\},\{s\},\{p,s\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{204}=\{\varnothing,\{p\},\{s\},\{p,s\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{205}=\{\varnothing,\{p\},\{s\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{206}=\{\varnothing,\{p\},\{p,q\},\{p,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{207}=\{\varnothing,\{p\},\{p,q\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{208}=\{\varnothing,\{p\},\{p,q\},\{p,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{209}=\{\varnothing,\{p\},\{p,q\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{210}=\{\varnothing,\{p\},\{p,r\},\{p,s\},\{p,q,r\},\{p,r,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{211}=\{\varnothing,\{p\},\{p,r\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{212}=\{\varnothing,\{q\},\{r\},\{p,q\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{213}=\{\varnothing,\{q\},\{r\},\{p,r\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{214}=\{\varnothing,\{q\},\{r\},\{q,r\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{215}=\{\varnothing,\{q\},\{r\},\{q,r\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{216}=\{\varnothing,\{q\},\{r\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{217}=\{\varnothing,\{q\},\{s\},\{p,q\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{218}=\{\varnothing,\{q\},\{s\},\{p,s\},\{q,s\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{219}=\{\varnothing,\{q\},\{s\},\{q,r\},\{q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{220}=\{\varnothing,\{q\},\{s\},\{q,s\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{221}=\{\varnothing,\{q\},\{s\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{222}=\{\varnothing,\{q\},\{p,q\},\{q,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{223}=\{\varnothing,\{q\},\{p,q\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{224}=\{\varnothing,\{q\},\{p,q\},\{q,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{225}=\{\varnothing,\{q\},\{p,q\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{226}=\{\varnothing,\{q\},\{q,r\},\{q,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{227}=\{\varnothing,\{q\},\{q,r\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{228}=\{\varnothing,\{r\},\{s\},\{p,r\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{229}=\{\varnothing,\{r\},\{s\},\{p,s\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{230}=\{\varnothing,\{r\},\{s\},\{q,r\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{231}=\{\varnothing,\{r\},\{s\},\{q,s\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{232}=\{\varnothing,\{r\},\{s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{233}=\{\varnothing,\{r\},\{p,r\},\{q,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{234}=\{\varnothing,\{r\},\{p,r\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{235}=\{\varnothing,\{r\},\{p,r\},\{r,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{236}=\{\varnothing,\{r\},\{p,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{237}=\{\varnothing,\{r\},\{q,r\},\{r,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{238}=\{\varnothing,\{r\},\{q,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{239}=\{\varnothing,\{s\},\{p,s\},\{q,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{240}=\{\varnothing,\{s\},\{p,s\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{241}=\{\varnothing,\{s\},\{p,s\},\{r,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{242}=\{\varnothing,\{s\},\{p,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{243}=\{\varnothing,\{s\},\{q,s\},\{r,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{244}=\{\varnothing,\{s\},\{q,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{245}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{246}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{247}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{248}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{249}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{250}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{251}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{252}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{253}=\{\varnothing,\{p\},\{q\},\{p,q\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{254}=\{\varnothing,\{p\},\{r\},\{p,q\},\{p,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{255}=\{\varnothing,\{p\},\{r\},\{p,q\},\{p,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{256}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{257}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{258}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{259}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{260}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{261}=\{\varnothing,\{p\},\{r\},\{p,r\},\{r,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{262}=\{\varnothing,\{p\},\{r\},\{p,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{263}=\{\varnothing,\{p\},\{s\},\{p,q\},\{p,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{264}=\{\varnothing,\{p\},\{s\},\{p,q\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{265}=\{\varnothing,\{p\},\{s\},\{p,r\},\{p,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{266}=\{\varnothing,\{p\},\{s\},\{p,r\},\{p,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{267}=\{\varnothing,\{p\},\{s\},\{p,s\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{268}=\{\varnothing,\{p\},\{s\},\{p,s\},\{q,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{269}=\{\varnothing,\{p\},\{s\},\{p,s\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{270}=\{\varnothing,\{p\},\{s\},\{p,s\},\{r,s\},\{p,q,s\},\{p,r,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{271}=\{\varnothing,\{p\},\{s\},\{p,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{272}=\{\varnothing,\{q\},\{r\},\{p,q\},\{q,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{273}=\{\varnothing,\{q\},\{r\},\{p,q\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{274}=\{\varnothing,\{q\},\{r\},\{p,r\},\{q,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{275}=\{\varnothing,\{q\},\{r\},\{p,r\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{276}=\{\varnothing,\{q\},\{r\},\{p,s\},\{q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{277}=\{\varnothing,\{q\},\{r\},\{q,r\},\{q,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{278}=\{\varnothing,\{q\},\{r\},\{q,r\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{279}=\{\varnothing,\{q\},\{r\},\{q,r\},\{r,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{280}=\{\varnothing,\{q\},\{r\},\{q,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{281}=\{\varnothing,\{q\},\{s\},\{p,q\},\{q,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{282}=\{\varnothing,\{q\},\{s\},\{p,q\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{283}=\{\varnothing,\{q\},\{s\},\{p,r\},\{q,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{284}=\{\varnothing,\{q\},\{s\},\{p,s\},\{q,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{285}=\{\varnothing,\{q\},\{s\},\{p,s\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{286}=\{\varnothing,\{q\},\{s\},\{q,r\},\{q,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{287}=\{\varnothing,\{q\},\{s\},\{q,r\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{288}=\{\varnothing,\{q\},\{s\},\{q,s\},\{r,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{289}=\{\varnothing,\{q\},\{s\},\{q,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{290}=\{\varnothing,\{r\},\{s\},\{p,q\},\{r,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{291}=\{\varnothing,\{r\},\{s\},\{p,r\},\{r,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{292}=\{\varnothing,\{r\},\{s\},\{p,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{293}=\{\varnothing,\{r\},\{s\},\{p,s\},\{r,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{294}=\{\varnothing,\{r\},\{s\},\{p,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{295}=\{\varnothing,\{r\},\{s\},\{q,r\},\{r,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{296}=\{\varnothing,\{r\},\{s\},\{q,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{297}=\{\varnothing,\{r\},\{s\},\{q,s\},\{r,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{298}=\{\varnothing,\{r\},\{s\},\{q,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{299}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},\{p,q,r\},S\}\\ &&\mathfrak{O}_{300}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,s\},\{q,s\},\{p,q,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{301}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r\},\{q,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{302}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,s\},\{q,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{303}=\{\varnothing,\{p\},\{r\},\{s\},\{p,r\},\{p,s\},\{r,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{304}=\{\varnothing,\{p\},\{r\},\{p,q\},\{p,r\},\{r,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{305}=\{\varnothing,\{p\},\{r\},\{p,r\},\{p,s\},\{q,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{306}=\{\varnothing,\{p\},\{s\},\{p,q\},\{p,s\},\{r,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{307}=\{\varnothing,\{p\},\{s\},\{p,r\},\{p,s\},\{q,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{308}=\{\varnothing,\{p\},\{p,q\},\{p,r\},\{p,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{309}=\{\varnothing,\{q\},\{r\},\{s\},\{q,r\},\{q,s\},\{r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{310}=\{\varnothing,\{q\},\{r\},\{p,q\},\{q,r\},\{r,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{311}=\{\varnothing,\{q\},\{r\},\{p,r\},\{q,r\},\{q,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{312}=\{\varnothing,\{q\},\{s\},\{p,q\},\{q,s\},\{r,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{313}=\{\varnothing,\{q\},\{s\},\{p,s\},\{q,r\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{314}=\{\varnothing,\{q\},\{p,q\},\{q,r\},\{q,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{315}=\{\varnothing,\{r\},\{s\},\{p,r\},\{q,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{316}=\{\varnothing,\{r\},\{s\},\{p,s\},\{q,r\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{317}=\{\varnothing,\{r\},\{p,r\},\{q,r\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{318}=\{\varnothing,\{s\},\{p,s\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{319}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{320}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{321}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{322}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,s\},\{q,s\},\{p,q,r\},\{p,q,s\},S\}\\ &&\mathfrak{O}_{323}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,s\},\{q,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{324}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,s\},\{q,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{325}=\{\varnothing,\{p\},\{q\},\{p,q\},\{p,r\},\{p,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{326}=\{\varnothing,\{p\},\{q\},\{p,q\},\{q,r\},\{q,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{327}=\{\varnothing,\{p\},\{r\},\{s\},\{p,r\},\{p,s\},\{r,s\},\{p,q,r\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{328}=\{\varnothing,\{p\},\{r\},\{s\},\{p,r\},\{p,s\},\{r,s\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{329}=\{\varnothing,\{p\},\{r\},\{s\},\{p,r\},\{p,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{330}=\{\varnothing,\{p\},\{r\},\{p,q\},\{p,r\},\{p,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ \end{eqnarray}$

$\begin{eqnarray} &&\mathfrak{O}_{331}=\{\varnothing,\{p\},\{r\},\{p,r\},\{q,r\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{332}=\{\varnothing,\{p\},\{s\},\{p,q\},\{p,r\},\{p,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{333}=\{\varnothing,\{p\},\{s\},\{p,s\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{334}=\{\varnothing,\{q\},\{r\},\{s\},\{q,r\},\{q,s\},\{r,s\},\{p,q,r\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{335}=\{\varnothing,\{q\},\{r\},\{s\},\{q,r\},\{q,s\},\{r,s\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{336}=\{\varnothing,\{q\},\{r\},\{s\},\{q,r\},\{q,s\},\{r,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{337}=\{\varnothing,\{q\},\{r\},\{p,q\},\{q,r\},\{q,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{338}=\{\varnothing,\{q\},\{r\},\{p,r\},\{q,r\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{339}=\{\varnothing,\{q\},\{s\},\{p,q\},\{q,r\},\{q,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{340}=\{\varnothing,\{q\},\{s\},\{p,s\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{341}=\{\varnothing,\{r\},\{s\},\{p,r\},\{q,r\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{342}=\{\varnothing,\{r\},\{s\},\{p,s\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{343}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{p,s\},\{q,r\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{344}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},\{q,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{345}=\{\varnothing,\{p\},\{q\},\{r\},\{p,q\},\{p,r\},\{q,r\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{346}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,r\},\{p,s\},\{q,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{347}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,s\},\{q,r\},\{q,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{348}=\{\varnothing,\{p\},\{q\},\{s\},\{p,q\},\{p,s\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{349}=\{\varnothing,\{p\},\{r\},\{s\},\{p,q\},\{p,r\},\{p,s\},\{r,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},S\}\\ &&\mathfrak{O}_{350}=\{\varnothing,\{p\},\{r\},\{s\},\{p,r\},\{p,s\},\{q,r\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{351}=\{\varnothing,\{p\},\{r\},\{s\},\{p,r\},\{p,s\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{352}=\{\varnothing,\{q\},\{r\},\{s\},\{p,q\},\{q,r\},\{q,s\},\{r,s\},\{p,q,r\},\{p,q,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{353}=\{\varnothing,\{q\},\{r\},\{s\},\{p,r\},\{q,r\},\{q,s\},\{r,s\},\{p,q,r\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{354}=\{\varnothing,\{q\},\{r\},\{s\},\{p,s\},\{q,r\},\{q,s\},\{r,s\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ &&\mathfrak{O}_{355}=\{\varnothing,\{p\},\{q\},\{r\},\{s\},\{p,q\},\{p,r\},\{p,s\},\{q,r\},\{q,s\},\{r,s\},\{p,q,r\},\{p,q,s\},\{p,r,s\},\{q,r,s\},S\}\\ \end{eqnarray}$

参考文献

集合・位相入門 p153