In mathematics, particularly topology, the homeomorphism group of a topological space is the group consisting of all homeomorphisms from the space to itself with function composition as the group operation. Homeomorphism groups are very important in the theory of topological spaces and in general are examples of automorphism groups. Homeomorphism groups are topological invariants in the sense that the homeomorphism groups of homeomorphic topological spaces are isomorphic as groups.
Read more about Homeomorphism Group: Properties and Examples, Mapping Class Group
Famous quotes containing the word group:
“A little group of willful men, representing no opinion but their own, have rendered the great government of the United States helpless and contemptible.”
—Woodrow Wilson (18561924)