Editing Commensurability (mathematics) (section)

==In topology==
Two [[path-connected]] [[topological space]]s are sometimes said to be ''commensurable'' if they have [[homeomorphism|homeomorphic]] finite-sheeted [[covering space]]s. Depending on the type of space under consideration, one might want to use [[homotopy|homotopy equivalences]] or [[diffeomorphism]]s instead of homeomorphisms in the definition. If two spaces are commensurable, then their [[fundamental group]]s are commensurable.

Example: any two [[closed surface]]s of [[genus (mathematics)|genus]] at least 2 are commensurable with each other.