nLab
proper action

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Representation theory

Contents

Definition

The action of a topological group GG on a topological space XX is called a proper action if the continuous function

G×X X×X (g,x) (gx,x) \array{ G \times X &\longrightarrow& X \times X \\ (g,x) &\mapsto& (g\cdot x, x) }

is a proper continuous function.

References

For instance

  • Marja Kankaanrinta, Def. 2.1 in Equivariant collaring, tubular neighbourhood and gluing theorems for proper Lie group actions, Algebr. Geom. Topol. Volume 7, Number 1 (2007), 1-27 (euclid:agt/1513796653)

See also

Last revised on February 6, 2019 at 10:54:22. See the history of this page for a list of all contributions to it.