A first-countable, compact space which is non-separable
32819
Looking for examples of first countable, compact spaces which is not separable
79779
How big can a separable Hausdorff space be?
22295
Subspace of a separable space is separable
105358
In a second countable space any base has a countable subset that is still a base
64375
Non-Metrizable Topological Spaces
92526
Collection of clopen sets form a base for a countable completely regular space
102048
Closure of a compact set in Regular space $ X $
98756
Unit ball in $C[0,1]$ not sequentially compact
97053
To prove $\omega_1 \cup \{\omega_1\} $ is not first countable but $\omega_1$ is
68994
Countable closed sets
149980
Are there any countable Hausdorff connected spaces?
95234
Quasi-components in compact space
109638
Show that a complete metric space without isolated points is uncountable
106606
How to prove that compact subspaces of the Sorgenfrey line are countable?
71916
Quasi-components and components coincide for compact Hausdorff spaces
64840
A Banach space that is not a Hilbert space
111360
Topological spaces in which every proper closed subset is compact