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".