New posts in Compactness

Is $\Bbb{Z}$ compact under the evenly spaced integer topology?

"Indexed" version of compactness and Axiom of Choice

Why is compactness required in Arzela Ascoli?

Let $X$ and $Y$ be metric spaces, $X$ compact, and $T: X \to Y$ bijective and continuous. Show that $T$ is a homeomorphism.

upper bound of outer measure on compact support of continuous function

$X \subset \mathbb{R}^n$ bounded $\implies f(X)$ is Bounded

If all closed subsets of a set are compact, does it follow that this set is subset of a compact set?

Giving a sequential proof of the Heine-Borel theorem

Could *I* have come up with the definition of Compactness (and Connectedness)?

Counterexample finite intersection property