# Compact space

### From Conservapedia

A topological space **X** is said to be compact, if every open cover of **X** contains a finite subcover.

**Important Theorem**: A metric space is compact if and only if it's complete and totally bounded.

A topological space **X** is said to be compact, if every open cover of **X** contains a finite subcover.

**Important Theorem**: A metric space is compact if and only if it's complete and totally bounded.