Infinite Closed Discrete Subset of a Normal non-compact Space
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
7402
Showing a compact metric space has a countable dense subset
111360
Topological spaces in which every proper closed subset is compact
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
99675
A closed ball in $l^{\infty}$ is not compact
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
128934
Every infinite Hausdorff space has an infinite discrete subspace
73154
Compact subset in colimit of spaces
65976
in a topological space only finite subsets are compact sets
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
92571
Sets with no asymptotical density over $\mathbb N$
110744
How to prove that a compact set in a Hausdorff topological space is closed?
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
106534
"Closed subsets of compact space are compact" with an alternative definition of covering
155621
Finiteness of the dimension of a normed space and compactness
149220
If every compact set is closed, then is the space Hausdorff?