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homeomorphism group
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.
==Properties and Examples==
There is a natural group action of the homeomorphism group of a space on that space. If this action is transitive, then the space is said to be homogeneous.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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