Homeomorphism
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In the mathematical field of topology, a homeomorphism or topological isomorphism or bicontinuous function (from the Greek words (homoios) = similar and (morph ) = shape, form) is a continuous function between two topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces that is, they are the mappings which 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. 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 joke is that topologists can't tell the coffee cup from which they are drinking from the donut they are eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786130267865
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T9mm
- Jahr 2009
- EAN 9786130267865
- Format Fachbuch
- ISBN 978-613-0-26786-5
- Titel Homeomorphism
- Untertitel Mathematics, Topology, Greek language, Continuous function, Topological space, Inverse function, Isomorphism, Category of topological spaces, Topological property, Geometry, Square (geometry)
- Gewicht 233g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 144
- Genre Mathematik
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