 As such, the composition of two homeomorphisms is again a homeomorphism, and the set of all self-homeomorphisms formula_34 forms a group, called the homeomorphism group of "X", often denoted formula_35.This group can be given a topology, such as the compact-open topology, which under certain assumptions makes it a topological group.For some purposes, the homeomorphism group happens to be too big, but by means of the isotopy relation, one can reduce this group to the mapping class group.