# nLab topological groupoid

## Theorems

#### Topology

topology

algebraic topology

# Contents

## Definition

### General

A topological groupoid is an internal groupoid in the category Top.

So this is a groupoid with a topological space of objects and one of morphisms, and all structure maps (source, target, identity, composition, inverse) are continuous maps.

A topological groupoid $C$ is called an open topological groupoid is the source map $s : Mor C \to Obj C$ is an open map.

It is called an étale groupoid if in addition $s$ is a local homeomorphism.

Revised on February 5, 2015 13:15:15 by Anonymous Coward (134.2.182.157)