Is every compact set is closed in any topological space?
106957
Compact sets are closed?
95993
Isn't every subset of a compact space compact?
120135
Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
28637
Proving continuous image of compact sets are compact
11383
Disjoint compact sets in a Hausdorff space can be separated
86782
A $T_4$ space satisfying that 'every continuous map from it to a Hausdorff space is a closed map' is compact.
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
121135
Why don't we use closed covers to define compactness of metric space?
34344
Is a function that maps every compact set to a compact set continuous?
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
138039
If $X$ is Hausdorff then every finite set is closed.
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
36237
Closed set mapped to itself in a compact Hausdorff space
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
147213
Prove that finite unions of compact sets are compact
55648
Intersection of finite number of compact sets is compact?