# Étale map

From Topospaces

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

## Contents

## Definition

Let and be topological spaces. A continuous map is termed an **étale map** if it is surjective, is a local homeomorphism, and if every fiber is discrete with the subspace topology.

## Relation with other properties

### Stronger properties

### Weaker properties

### Incomparable properties

- Bundle map (the map associated to a fiber bundle): A map which is both an etale map and a bundle map is a covering map