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''.<ref>{{cite web |url=https://mathoverflow.net/questions/110407 |title=Characterization of cocompact group actione |publisher=MathOverflow |access-date=2026-04-25}}</ref> It is sometimes referred to as ''mpact'', a tongue-in-cheek reference to dual notions where prefixing with "co-" twice would "cancel out".

==References== {{Reflist}}

* {{cite book|author1-link=Robert Daverman | title=Handbook of Geometric Topology | first1=Robert J. | last1=Daverman | first2=R. B. | last2=Sher | publisher=Elsevier | year=2002 | isbn=0444824324 | page=272 }}

{{DEFAULTSORT:Cocompact Group Action}} Category:Group actions