# Hemicompact space

From Topospaces

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

## Contents

## Definition

### Symbol-free definition

A topological space is termed **hemicompact** if it is the union of an ascending sequence of compact subsets, each contained in the interior of the next, such that every compact subset is contained in one of these.

### Definition with symbols

A topological space is termed **hemicompact** if there is a sequence of compact subsets such that , and such that any compact subset is contained in for some .