 Cocompact group action

A group action on a space is cocompact when its quotient is compact, equivalently when some compact set has translates covering the space.

A **cocompact group action** refers to a specific type of action of a group on a topological space, particularly in the context of topological groups and geometric topology. In broad terms, if a group \( G \) acts on a topological space \( X \), we say that the action is **cocompact** if the quotient space \( X/G \) is compact.