$X$ Hausdorff $\Leftrightarrow$ $\forall$ disjoint compacts $K_1,K_2:\exists$disjoint open sets $U,V$ including $K_1,K_2$ respectively
11383
Disjoint compact sets in a Hausdorff space can be separated
36237
Closed set mapped to itself in a compact Hausdorff space
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?
41408
Which of the following sets are compact:
77480
Is the set $S=\left\{\left(z_1,z_2\right)\in \mathbb C\times \mathbb C:z_1^2+z_2^2=1\right\}.$ compact?
37092
Homeomorphism between a cone in a compact space and this compactification
113534
Show that any metrizable space $X$ is Hausdorff
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
123090
How to show that disjoint closed sets have disjoint open supersets?
65180
A compact Hausdorff space that is not metrizable
89506
Union of disjoint sets : Equivalence relations
147213
Prove that finite unions of compact sets are compact
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
80996
A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
145415
Examples of almost compact spaces.
8015
Compact set plus a closed set is a closed set
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable