## 2018年11月5日月曜日

### 数学 - 集合と位相 - 位相空間 - 位相空間(3つの元からなる集合の全ての位相、密着位相から離散位相(ディスクリート位相(discrete topology))まで)

1. 濃度（個数）2。 （密着位相）

$\left\{\varphi ,S\right\}$

濃度（個数）3。

$\begin{array}{}\left\{\varphi ,\left\{p\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},S\right\}\\ \left\{\varphi ,\left\{r\right\},S\right\}\\ \left\{\varphi ,\left\{p,q\right\},S\right\}\\ \left\{\varphi ,\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{q,r\right\},S\right\}\end{array}$

濃度4。

$\begin{array}{}\left\{\varphi ,\left\{p\right\},\left\{p,q\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{p,q\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{r\right\},\left\{p,q\right\},S\right\}\\ \left\{\varphi ,\left\{r\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{r\right\},\left\{q,r\right\},S\right\}\end{array}$

濃度5。

$\begin{array}{}\left\{\varphi ,\left\{p\right\},\left\{q\right\},\left\{p,q\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{r\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{r\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{p,q\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{p,q\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{r\right\},\left\{p,r\right\},\left\{q,r\right\},S\right\}\end{array}$

濃度6。

$\begin{array}{}\left\{\varphi ,\left\{p\right\},\left\{q\right\},\left\{p,q\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{q\right\},\left\{p,q\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{r\right\},\left\{p,q\right\},\left\{p,r\right\},S\right\}\\ \left\{\varphi ,\left\{p\right\},\left\{r\right\},\left\{p,r\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{r\right\},\left\{p,q\right\},\left\{q,r\right\},S\right\}\\ \left\{\varphi ,\left\{q\right\},\left\{r\right\},\left\{p,r\right\},\left\{q,r\right\},S\right\}\end{array}$

濃度8。（離散位相、ディスクリート位相）

$P\left(\left\{p,q,r\right\}\right)$

以上で29個。