nLab
relatively compact subspace

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

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

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