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Topology

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Facts About Topologies

TOPO-MKZBJN

Let $(X,\tau)$ be a topological space. Which of the following are TRUE?

Select ALL that apply.

A

If $A\subseteq \tau$, then $\{x\in X : x\in U$ for some $U\in A\}\in\tau$

B

If $A\subseteq \tau$, then $\{x\in X : x\in U$ for all $U\in A\}\in\tau$

C

If $A\subseteq \tau$ is finite, then $\{x\in X : x\in U$ for some $U\in A\}\in\tau$

D

If $A\subseteq \tau$ is finite, then $\{x\in X : x\in U$ for all $U\in A\}\in\tau$

E

$X\in\tau$