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- Homeomorphism abstract "In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word homeomorphism comes from the Greek words ὅμοιος (homoios) = similar and μορφή (morphē) = shape, form.Roughly speaking, a topological space is a geometric object, and the homeomorphism is a continuous stretching and bending of the object into a new shape. Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not. An often-repeated mathematical joke is that topologists can't tell their coffee cup from their donut, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while preserving the donut hole in a cup's handle.Topology is the study of those properties of objects that do not change when homeomorphisms are applied. As Henri Poincaré famously said, mathematics is not the study of objects, but, instead, the relations (isomorphisms for instance) between them.".
- Homeomorphism thumbnail Mug_and_Torus_morph.gif?width=300.
- Homeomorphism wikiPageID "13660".
- Homeomorphism wikiPageRevisionID "604879190".
- Homeomorphism hasPhotoCollection Homeomorphism.
- Homeomorphism id "912".
- Homeomorphism id "p/h047600".
- Homeomorphism title "Homeomorphism".
- Homeomorphism subject Category:Functions_and_mappings.
- Homeomorphism subject Category:Homeomorphisms.
- Homeomorphism type Abstraction100002137.
- Homeomorphism type Function113783816.
- Homeomorphism type FunctionsAndMappings.
- Homeomorphism type MathematicalRelation113783581.
- Homeomorphism type Relation100031921.
- Homeomorphism comment "In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.".
- Homeomorphism label "Homeomorfisme".
- Homeomorphism label "Homeomorfismo".
- Homeomorphism label "Homeomorfismo".
- Homeomorphism label "Homeomorfizm".
- Homeomorphism label "Homeomorphism".
- Homeomorphism label "Homéomorphisme".
- Homeomorphism label "Homöomorphismus".
- Homeomorphism label "Omeomorfismo".
- Homeomorphism label "Гомеоморфизм".
- Homeomorphism label "دالة هميومرفية".
- Homeomorphism label "位相同型".
- Homeomorphism label "同胚".
- Homeomorphism sameAs Homeomorfismus.
- Homeomorphism sameAs Homöomorphismus.
- Homeomorphism sameAs Homeomorfismo.
- Homeomorphism sameAs Homéomorphisme.
- Homeomorphism sameAs Homeomorfisma.
- Homeomorphism sameAs Omeomorfismo.
- Homeomorphism sameAs 位相同型.
- Homeomorphism sameAs 위상동형사상.
- Homeomorphism sameAs Homeomorfisme.
- Homeomorphism sameAs Homeomorfizm.
- Homeomorphism sameAs Homeomorfismo.
- Homeomorphism sameAs m.03k7d.
- Homeomorphism sameAs Q202906.
- Homeomorphism sameAs Q202906.
- Homeomorphism sameAs Homeomorphism.
- Homeomorphism wasDerivedFrom Homeomorphism?oldid=604879190.
- Homeomorphism depiction Mug_and_Torus_morph.gif.
- Homeomorphism isPrimaryTopicOf Homeomorphism.
