nLab
proper topological groupoid

Contents

Definition

A topological groupoid X 1tsX 0X_1 \stackrel{\overset{s}{\to}}{\underset{t}{\to}} X_0 is called proper if the continuous map

(s,t):X 1X 0×X 0 (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)