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homeomorphisms
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Definitions of homeomorphisms in various dictionaries:
HOMEOMORPHISMS - In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topologi...
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Plural form of homeomorphism. |
An instance of topological equivalence. |
Homeomorphisms description |
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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 spacesthat 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 (homoios) = similar or same and (morph) = shape, form, introduced to mathematics by Henri Poincaré in 1895.Very 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 torus are not. However, this description can be misleading. Some continuous deformations are not homeomorphisms, s |