Self-homeomorphism group

Definition
The self-homeomorphism group of a topological space is defined in the following equivalent ways:


 * It is the group of homeomorphisms from the topological space to itself, under composition
 * It is the automorphism group of the topologicla space, viewed as an object in the category of topological space with continuous maps

The association of a self-homeomorphism group to a topological space is not functorial.

Related notions

 * Mapping class group is the quotient of the self-homeomorphism group, by the group of self-homeomorphisms isotopic to the identity map.