when compactness implies finiteness
65976
in a topological space only finite subsets are compact sets
146146
Proof that a closed subset of a compact space is a compact space
18596
A set $A \subset l_1$ is compact if and only if closed, bounded, and one other condition
124959
Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
148992
A finite set is closed
135157
Totally bounded, complete $\implies$ compact
45792
Rigorous proof that surjectivity implies injectivity for finite sets
81927
Example of closed and bounded in $\mathbb Q$ set that is not compact
145415
Examples of almost compact spaces.
3708
How can I prove that compact subset iff sequentially compact in second countable topological spaces?
6210
Countable compact spaces as ordinals
64694
$C_{c}(X)$ is complete. then implies that $X$ is compact.
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
50611
Question about Stone-Čech compactification
88508
References for quasi finite and proper implies finite
80414
Countable Product of Sequentially Compact spaces is Sequentially Compact