Sigma-compact space: Difference between revisions
No edit summary |
|||
| Line 7: | Line 7: | ||
===Symbol-free definition=== | ===Symbol-free definition=== | ||
A [[topological space]] is said to be '''sigma-compact''' or <math>\sigma</math>-compact if it has a countable collection of subsets such that the union of their interiors is the whole space. | A [[topological space]] is said to be '''sigma-compact''' or <math>\sigma</math>-compact if it has a countable collection of compact subsets such that the union of their interiors is the whole space. | ||
==Relation with other properties== | ==Relation with other properties== | ||
Revision as of 23:57, 20 December 2007
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of compactness. View other variations of compactness
Definition
Symbol-free definition
A topological space is said to be sigma-compact or -compact if it has a countable collection of compact subsets such that the union of their interiors is the whole space.