$A$ compact $\implies$ $\overline{A}$ compact?
37654
Topology: Example of a compact set but its closure not compact
116663
If f is a continuous map from X to Y with X limit point compact, does it follow that f(X) is limit point compact?
31741
Show for $f:A \to Y$ uniformly continuous exists a unique extension to $\overline{A}$, which is uniformly continuous
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
70017
Every subspace of a compact space is compact?
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
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
127173
Closed subset of compact set is compact
29474
Compactness of $\operatorname{Spec}(A)$
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
37850
Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval?
50611
Question about Stone-Čech compactification
64694
$C_{c}(X)$ is complete. then implies that $X$ is compact.
106434
Prove that for a dense set $A$ and an open set $U$, $U\subset \overline{A\cap U}$
39842
Limit point Compactness does not imply compactness counter-example
31747
Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space