logo

Equivalence of Various Compactnesses in Metric Spaces 📂MetricSpace

Equivalence of Various Compactnesses in Metric Spaces

Theorem1

Let $X$ be a metric space. The following propositions are equivalent.

Explanation

This generally does not hold in topological spaces but holds in metric spaces.


  1. 박대희·안승호, 위상수학(하) (5/E, 2022), p503 ↩︎