A counterexample to the Sura-Bura Theorem for non separated compact spaces
95234
Quasi-components in compact space
64840
A Banach space that is not a Hilbert space
99675
A closed ball in $l^{\infty}$ is not compact
96717
Hahn-Banach Theorem for separable spaces without Zorn's Lemma
88099
Not $\sigma$-compact set without axiom of choice
39842
Limit point Compactness does not imply compactness counter-example
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
156161
Banach-Tarski theorem without axiom of choice
147331
Compactness and Hausdorffness
125623
Subspaces of separable normed spaces
147213
Prove that finite unions of compact sets are compact
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
9268
Proving that the Union of Two Compact Sets is Compact
11383
Disjoint compact sets in a Hausdorff space can be separated
138607
Proof that a limit point compact metric space is compact.