E is closed. K is compact. Show that every open cover of $E\cap K$ has a finite subcover
140570
Suppose $E\subseteq\mathbb{R}$ is closed and $K\subseteq\mathbb{R}$ is compact. Show that every open cover of $E\cap K$ has a finite subcover
54346
If $G$ is a compact topological group, how to show that a finite index subgroup of $G$ is open?
83311
Compactness of $A:=${$f \in C[0,1], |f|_\infty \le K, |f'|_\infty \le M$}
16826
prove that every infinite subset of compact set H has a limit point (Explanation)
55648
Intersection of finite number of compact sets is compact?
69367
covering map with finite fibres and preimage of a compact set
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
147197
Number of connected components of the complement of a compact
147213
Prove that finite unions of compact sets are compact
111008
Show that $X $ is a infinite set ,it is connected in the finite complement topology?
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
146146
Proof that a closed subset of a compact space is a compact space
9268
Proving that the Union of Two Compact Sets is Compact
78117
Closed property of nonempty finite set
135256
The fiber of a covering space over a connected space has constant cardinality
80180
Discrete and compact subset must be finite
147914
Closed image of locally compact space