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)