Isn't every subset of a compact space compact?
70017
Every subspace of a compact space is compact?
28637
Proving continuous image of compact sets are compact
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
50611
Question about Stone-Čech compactification
36631
Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?
58285
Is it true that if $X$ is connected, then for every nonempty proper subset $A$ of $X$, we have $\mathbf{Bd} \ne \emptyset$
7402
Showing a compact metric space has a countable dense subset
106534
"Closed subsets of compact space are compact" with an alternative definition of covering
157565
Is every dense subspace of a separable space separable?
37654
Topology: Example of a compact set but its closure not compact
481
Can compact sets completey determine a topology?
135157
Totally bounded, complete $\implies$ compact
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
35652
Every compact metric space is complete
148187
Question regarding one-point compactification and homeomorphisms
9268
Proving that the Union of Two Compact Sets is Compact