Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
44259
Heine-Borel Theorem ($\mathbb{R}^k$) (in ZF)
154578
Proving there is a sequence convergent to a limit point of a set without axiom of countable choice?
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
36237
Closed set mapped to itself in a compact Hausdorff space
66334
How is every subset of the set of reals with the finite complement topology compact?
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
94485
Limit point compactness implies compactness.
95993
Isn't every subset of a compact space compact?
37654
Topology: Example of a compact set but its closure not compact
8015
Compact set plus a closed set is a closed set
69650
In $\mathbb{R}^n$, locally lipschitz on compact set implies lipschitz
106957
Compact sets are closed?
47810
$C(X)$ is separable when $X$ is compact?
126463
Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic?
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
18040
Show that a compact metric space is bounded