Hausdorff

Definition Let $(X, \tau)$ be a . Then $X$ is if for every $x, y \in X$ there exist $U,...

11/7/2022

Topological Space

Definition Let $X$ be a and $\tau \subset \mathcal{P}(X)$. Then $(X, \tau)$ is a if $X, \emptyset \in \tau$. Suppose $F...

11/7/2022

Compact

Definition Let $X$ be a . We say $K \subset X$ is if every of $K$ can be reduced...

11/7/2022

Open

Definition Suppose $(X, \tau)$ is a . Then $U \subset X$ is if $U \in \tau$....

11/7/2022

Compact Sets are Separable from Points in a Hausdorff Space

Statement Let $X$ be a . Then if $K \subset X$ is and $y \not\in X$, then there exists...

11/7/2022

Open Cover

Definition Let $X$ be a , $I \preccurlyeq \mathcal{P}(X)$ be an , and $S \subset X$. An of $S$ is...

11/7/2022