$K\subseteq X$ compact, C closed, can I say something about $K \cap C$?
14219
Is the intersection of a closed set and a compact set always compact?
150337
Let $K$ be a subfield of $\mathbb{C}$ not contained in $\mathbb{R}$. Show that $K$ is dense in $\mathbb{C}$.
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
135157
Totally bounded, complete $\implies$ compact
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?
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
39293
Given a compact set $K$ and closed set $E,$ prove: $E\cap K\neq \emptyset $
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
147213
Prove that finite unions of compact sets are compact
88099
Not $\sigma$-compact set without axiom of choice
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
149220
If every compact set is closed, then is the space Hausdorff?
41408
Which of the following sets are compact:
12467
Why does this proof work: Closed unit ball in $C_0$ is not compact
73353
Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?