How to prove that every countable compact Hausdorff space is homeomorphic to a well-ordered set with its order topology?
6210
Countable compact spaces as ordinals
37092
Homeomorphism between a cone in a compact space and this compactification
136094
$G_\delta$ singletons in compact Hausdorff and first countability
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
7678
Show "countable complement topology" is a topology
44974
Infinite set and countable subsets
9021
An infinite subset of a countable set is countable
88028
Topology - closures of intervals with the order topology
147350
Homeomorphism between $\prod X_i$ and the Cantor set
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?
46970
If $X$ is compact and $T:X \to Y$ continuous and bijective, show that $T$ is homeomorphism.
18223
Prove that the union of two disjoint countable sets is countable
94438
Show that the countable product of metric spaces is metrizable
16649
Topological space with countable open cover $\{U_\alpha\} $ with each $U_\alpha$ second-countable, is second countable
148187
Question regarding one-point compactification and homeomorphisms
19297
Is the cofinite topology on an uncountable set first countable?
91237
Every infinite set contains a countable subset