Self-homeomorphism group

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This article defines an association of a group to every topological space. The association is not necessarily functorial


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

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.