nLab proper topological groupoid

Context

Topology

topology

algebraic topology

category theory

Contents

Definition

A topological groupoid $X_1 \stackrel{\overset{s}{\to}}{\underset{t}{\to}} X_0$ is called proper if the continuous map

$(s,t):X_1 \to X_0\times X_0$

is a proper map.

Properties

In particular the automorphism group of any object in a proper topological groupoid is a compact group. In this sense proper topological groupoids generalize compact groups.

Examples

A Lie groupoid is called a proper Lie groupoid if its underlying topological groupoid is proper.

An orbifold is a proper Lie groupoid which is also an étale groupoid.

Revised on February 2, 2012 11:44:25 by Urs Schreiber (82.169.65.155)