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There is a page named "Homeomorphism group" on Wikipedia
{\displaystyle X} and Y {\displaystyle Y} are homeomorphic. A self-homeomorphism is a homeomorphism from a topological space onto itself. Being "homeomorphic"...13 KB (1,640 words) - 15:11, 11 April 2024- mathematics, particularly topology, the homeomorphism group of a topological space is the group consisting of all homeomorphisms from the space to itself with function...3 KB (494 words) - 19:37, 31 August 2024
Homogeneous space (category Topological groups)group elements are assumed to act as homeomorphisms on X. The structure of a G-space is a group homomorphism ρ : G → Homeo(X) into the homeomorphism group...15 KB (1,821 words) - 03:07, 6 August 2024
Torus (redirect from Torus group)fundamental group); all homotopy equivalences of the torus can be realized by homeomorphisms – every homotopy equivalence is homotopic to a homeomorphism. Thus...38 KB (5,046 words) - 18:10, 15 August 2024
spaces, Top. Representations in Top are homomorphisms from G to the homeomorphism group of a topological space X. Two types of representations closely related...15 KB (2,136 words) - 13:51, 22 June 2024
Automorphism (section Automorphism group)automorphism of a topological space is a homeomorphism of the space to itself, or self-homeomorphism (see homeomorphism group). In this example it is not sufficient...11 KB (1,330 words) - 15:05, 11 April 2024
Isometry (redirect from Group of isometries)isomorphism Euclidean plane isometry Flat (geometry) Homeomorphism group Involution Isometry group Motion (geometry) Myers–Steenrod theorem 3D isometries...18 KB (2,351 words) - 20:34, 29 July 2024
isomorphism that is also a homeomorphism of the underlying topological spaces. This is stronger than simply requiring a continuous group isomorphism—the inverse...50 KB (7,492 words) - 16:51, 25 May 2024
Covering space (redirect from Deck transformation group)there exists a homeomorphism h : E → E ′ {\displaystyle h:E\rightarrow E'} , such that the diagram commutes. If such a homeomorphism exists, then one...38 KB (6,950 words) - 01:25, 22 July 2024- contractible, the fundamental group of GL+(n, R) is isomorphic to that of SO(n). The homeomorphism also shows that the group GL(n, R) is noncompact. “The”...23 KB (2,965 words) - 00:14, 1 September 2024
The precise locations of the holes are irrelevant, because the homeomorphism group acts k-transitively on any connected manifold of dimension at least...32 KB (4,170 words) - 23:57, 20 April 2024
Representation theory (section Finite groups)spaces, Top. Representations in Top are homomorphisms from G to the homeomorphism group of a topological space X. Three types of representations closely...55 KB (7,184 words) - 17:41, 8 July 2024- restricts onto a homeomorphism of the complements of the knots, and this restricted homeomorphism induces an isomorphism of fundamental groups. However, it...3 KB (389 words) - 14:32, 13 July 2022
- space G \ X. Now assume G is a topological group and X a topological space on which it acts by homeomorphisms. The action is said to be continuous if the...46 KB (5,637 words) - 12:41, 27 June 2024
- identity map and the constant maps to 0 and 1. It follows that the homeomorphism group of S is trivial. Let X be an arbitrary set. The set of all functions...13 KB (1,918 words) - 04:08, 9 June 2024
- the mapping class group of a surface, sometimes called the modular group or Teichmüller modular group, is the group of homeomorphisms of the surface viewed...31 KB (4,595 words) - 03:39, 1 November 2023
- actions on manifolds by homeomorphisms or diffeomorphisms. The groups themselves may be discrete or continuous. Most groups considered in the first stage...40 KB (5,204 words) - 12:00, 26 May 2024
- every point b in B admits an open neighborhood U such that there is a homeomorphism between the preimage of U and a disjoint union of copies of U (indexed...53 KB (8,076 words) - 07:10, 6 August 2024
Diffeomorphism (redirect from Diffeomorphism group)a homeomorphism, f {\displaystyle f} and its inverse need only be continuous. Every diffeomorphism is a homeomorphism, but not every homeomorphism is...25 KB (4,165 words) - 15:27, 23 February 2024- does not bound a Möbius strip, the y-homeomorphism of Lickorish, and the product of the twist and the y-homeomorphism. It is a nice exercise to show that...17 KB (2,383 words) - 08:19, 30 July 2024
- fact, they may be defined as functions which can be made analytic by a homeomorphism of the domain of definition. Quasi-conformal functions ... are interior
- {\displaystyle f_{*}:H_{n}(X)\to H_{n}(Y)} . If f {\displaystyle f} is a homeomorphism, f ∗ {\displaystyle f_{*}} is an isomorphism. (under construction) (under