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category of topological spaces
Homeomorphisms
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Summary Of: Homeomorphism

Two spaces with a homeomorphism between them are called... and the homeomorphism is a continuous stretching and bending of the object into a new shape... a homeomorphism maps points in the first object that are... is a homeomorphism of a topological space and itself... of a continuous bijection that is not a homeomorphism is the map that takes the half... the homeomorphism group happens to be too big... A homeomorphism is simultaneously an... homeomorphism of the whole disk... This characterization of a homeomorphism often leads to confusion with the concept of...

Encyclodia Page On: Homeomorphism

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homomorphism | topological equivalence (dynamical systems) | A continuous deformation between a coffee mug and a donut illustrating that they are homeomorphic. But there does not need to be a continuous deformation for two spaces to be homeomorphic. | | donut | mathematical | topology | Greek | bicontinuous function | topological spaces | isomorphisms | category of topological spaces | mappings | topological properties | geometric | square | circle | sphere | donut | function | topological spaces | bijection | 1-1 | onto | continuous | inverse function | open mapping | equivalence relation | class | equivalence classes | A trefoil knot is homeomorphic to a circle. While this may seem illogical, in four dimensions they can easily be deformed continuously. Here the knot has been thickened to make the image understandable. | | trefoil knot | disc | unit square | interval | real numbers | product space | S1 | dimensional | torus | uniform isomorphism | isometric isomorphism | 2-sphere | plane | isomorphisms | category of topological spaces | group | isotopy | mapping class group | topological properties | compact | connected | Hausdorff | homology groups | metric | complete | open mapping | closed mapping | open sets | closed sets | Alexander's Trick | line segment | homotopy | homotopy equivalence | isotopy | identity map | Local homeomorphism | Diffeomorphism | Uniform isomorphism | uniform spaces | Isometric isomorphism | metric spaces | Dehn twist | Homeomorphism (graph theory) | Isotopy | Mapping class group | PlanetMath | Categories | Homeomorphisms | Functions and mappings |
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Homeomorphism".