Proof of compact sets
140741
Generalized Tube Lemma
79531
Distance between sets with one closed set and one compact set
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
41192
Neatest proof that set of finite subsets is countable?
147331
Compactness and Hausdorffness
69367
covering map with finite fibres and preimage of a compact set
65358
Prove $X$ is compact iff for each family $\{ F_\alpha\}_{\alpha\in I}$ of closed subsets of $X$ with the FIP, we have $\cap F_\alpha\neq\varnothing$.
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
158882
Prove the existence of some weird family of sets
151686
A proof that the Cantor set is Perfect
128457
Show that $T$ is a compact operator
73154
Compact subset in colimit of spaces
102048
Closure of a compact set in Regular space $ X $
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
45792
Rigorous proof that surjectivity implies injectivity for finite sets
8015
Compact set plus a closed set is a closed set