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Summary Of: Homeomorphic

are homeomorphic to each other... A trefoil knot is homeomorphic to a circle... A trefoil knot is homeomorphic to a circle... is homeomorphic to a circle... with a single point removed is homeomorphic to the set of all points in... Two homeomorphic spaces share the same... there are metric spaces which are homeomorphic even though one of them is...

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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 "Homeomorphic".