Intersection of a closed set and compact set is compact
14219
Is the intersection of a closed set and a compact set always compact?
48783
Prove that the sum of two compact sets in $\mathbb R^n$ is compact.
138607
Proof that a limit point compact metric space is compact.
144400
Are compact subsets of metric spaces closed and bounded?
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
9268
Proving that the Union of Two Compact Sets is Compact
153573
Counter Example for the union of any number of compact sets is compact in T2-spaces
147914
Closed image of locally compact space
43376
If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
64694
$C_{c}(X)$ is complete. then implies that $X$ is compact.
141642
Closure of a certain subset in a compact topological group
48162
Is the subset $[0, \sqrt2] ∩\mathbb{Q} ⊂ \mathbb{Q}$ closed, bounded, compact?
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
133086
When Cantor's Intersection theorem won't work with closed sets
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
50026
Product of compact and closed in topological group is closed