Intersection of two compact sets in $\mathbb R$ is compact (without Heine-Borel theorem)
9268
Proving that the Union of Two Compact Sets is Compact
64861
Intersection of open affines can be covered by open sets distinguished in *both*affines
66180
Homomorphism between compact Hausdorff spaces.
31559
If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
147213
Prove that finite unions of compact sets are compact
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
88099
Not $\sigma$-compact set without axiom of choice
152193
The intersection of a closure with an open set
147331
Compactness and Hausdorffness
131037
Is every compact subset of $\Bbb{R}$ the support of some Borel measure?
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
110744
How to prove that a compact set in a Hausdorff topological space is closed?
10531
Is the convex hull of a compact set compact?
28683
Sum of two closed sets in $\mathbb R$ is closed?
86309
Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition