The homeomorphism group of a topological space is the set of all homeomorphisms , which forms a group by composition.
Homeomorphism Group
See also
Group, Infinite Group, Topological SpaceThis entry contributed by Todd Rowland
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Rowland, Todd. "Homeomorphism Group." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HomeomorphismGroup.html