# Cocompact group action

In mathematics, an action of a group *G* on a topological space *X* is **cocompact** if the quotient space *X*/*G* is a compact space. If *X* is locally compact, then an equivalent condition is that there is a compact subset *K* of *X* such that the image of *K* under the action of *G* covers *X*. It is sometimes referred to as *mpact*, a tongue-in-cheek reference to dual notions where prefixing with "co-" twice would "cancel out".

## References

- Daverman, Robert J.; Sher, R. B. (2002).
*Handbook of Geometric Topology*. Elsevier. p. 272. ISBN 0444824324.

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