General topology Continuous maps Concept
Homeomorphism
Summary
A homeomorphism is a continuous bijection between topological spaces whose inverse is also continuous. Homeomorphic spaces are the same from the point of view of topology.
Where this leads
83 pages build on this one.
- Kuranishi structure
- Jordan–Brouwer separation theorem
- Suspension
- Brouwer's characterization of the Cantor space
- Poincaré conjecture
- Schoenflies theorem
- Mapping class group
- Fiber bundle
- Expansive homeomorphism
- Stable homotopy theory
- Poincaré classification of circle homeomorphisms
- Circle map
- Banach bundle
- Triangulability of analytic sets
- Invariance of domain
- Absolute neighborhood retract
- Thom–Mather isotopy lemmas
- Sphere theorem
- Local homeomorphism
- Hauptvermutung
- Generalized Poincaré conjecture
- Shift space
- Quasiconformal mapping
- Topological homogeneity
- Fréchet manifold
- Radó's theorem on triangulation of surfaces
- Closed immersion
- Topological conjugacy
- Gordon–Luecke theorem
- Anosov flow
- Manifold with corners
- Knot
- Thom spectrum
- Fredholm map
- Rotation number
- Annulus theorem
- Isomorphism of topological groups
- Freedman's classification of simply connected 4-manifolds
- Smooth dynamical system
- Triangulation conjecture
- Lê–Ramanujam theorem
- Local trivialization
- Poincaré–Birkhoff theorem
- Pseudogroup
- Structural stability
- Wandering set
- Link of a singularity
- Surface
- Hilbert manifold
- Quasicircle
- Nielsen–Thurston classification
- Complex manifold
- Atlas
- Dehn surgery
- Banach–Stone theorem
- Cardinal function
- Alexander horned sphere
- Triangulation
- Wild knot
- Suspension flow
- Toda bracket
- Deck transformation group
- Link
- Measurable Riemann mapping theorem
- Banach–Lie group
- Banach manifold
- Smooth structure
- Bing–Borsuk conjecture
- Properly discontinuous action
- Smooth manifold
- Pseudo-Anosov map
- Borel conjecture
- Stability conjecture
- Dehn twist
- Covering space
- Manifold with boundary
- Spectrum
- Anderson–Kadec theorem
- 3-manifold
- Topological manifold
- Finite-dimensional Hausdorff vector topologies are Euclidean
- Zariski's multiplicity conjecture
- Open immersion
Further reading
- Web https://en.wikipedia.org/wiki/Homeomorphism, lead section
About this page
| Tag | 0QT00PB5G2 |
|---|---|
| URI | m2://0QT00PB5G2 |
| Aliases | topological-isomorphism, homeomorphic-spaces |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54C05 |
| Specializes | Continuous map, Open map, Closed map |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Special cases
Used by
- Kuranishi structure
- Jordan–Brouwer separation theorem
- Suspension
- Brouwer's characterization of the Cantor space
- Poincaré conjecture
- Schoenflies theorem
- Mapping class group
- Fiber bundle
- Expansive homeomorphism
- Poincaré classification of circle homeomorphisms
- Circle map
- Banach bundle
- Triangulability of analytic sets
- Invariance of domain
- Absolute neighborhood retract
- Thom–Mather isotopy lemmas
- Sphere theorem
- Local homeomorphism
- Hauptvermutung
- Generalized Poincaré conjecture
- Shift space
- Quasiconformal mapping
- Topological homogeneity
- Fréchet manifold
- Closed immersion
- Topological conjugacy
- Gordon–Luecke theorem
- Manifold with corners
- Knot
- Rotation number
- Annulus theorem
- Isomorphism of topological groups
- Freedman's classification of simply connected 4-manifolds
- Triangulation conjecture
- Lê–Ramanujam theorem
- Local trivialization
- Poincaré–Birkhoff theorem
- Pseudogroup
- Structural stability
- Wandering set
- Link of a singularity
- Surface
- Nielsen–Thurston classification
- Complex manifold
- Atlas
- Dehn surgery
- Banach–Stone theorem
- Cardinal function
- Triangulation
- Wild knot
- Suspension flow
- Deck transformation group
- Link
- Banach manifold
- Smooth structure
- Bing–Borsuk conjecture
- Properly discontinuous action
- Smooth manifold
- Pseudo-Anosov map
- Borel conjecture
- Dehn twist
- Covering space
- Manifold with boundary
- Anderson–Kadec theorem
- 3-manifold
- Topological manifold
- Finite-dimensional Hausdorff vector topologies are Euclidean
- Zariski's multiplicity conjecture
- Open immersion