# nLab relatively compact subspace

A subset $A$ of a topological space $X$ is relatively compact if its closure $\bar{A}$ is compact. We also say that $A$ with its induced topology is a relatively compact subspace of $X$.

The relatively compact subsets of a Hausdorff space $X$ form an ideal in the power set of $X$.

Revised on January 14, 2010 20:51:31 by Toby Bartels (169.235.55.112)