# Proper map

From Topospaces

*This article defines a property of continuous maps between topological spaces*

## Contents

## Definition

### Symbol-free definition

A continuous map of topological spaces is termed a **proper map** if it is closed and the inverse image of any compact subset in the image set, is a compact subset of the domain. Equivalently, it is a closed map and the inverse image of any point is a compact subset of the domain.