カテゴリー: 位相の集合

\[ X^{s}=\left\{ x\in X;\left\{ x\right\} \in\mathcal{O}\right\} \]

\[ A^{d}=\left\{ x\in A;\left\{ x\right\} \notin\mathcal{O}_{A},\right\} \cup\left(A^{f}\setminus A\right) \]

\[ A^{i}\cup B^{i}\subseteq\left(A\cup B\right)^{i} \]

\[ A^{d}=\emptyset\Leftrightarrow\forall x\in X,\exists U_{x}\in\mathcal{O},U_{x}\cap A\subseteq\left\{ x\right\} \]

\[ \exists U_{x}\in\mathcal{O},U_{x}\subseteq A \]

\[ A^{i}\subseteq A \]