Definitions for Homeomorphism
ˌhoʊ mi əˈmɔr fɪz əmho·meo·mor·phism

WiktionaryRate this definition:0.0 / 0 votes

1. homeomorphismnoun

   a continuous bijection from one topological space to another, with continuous inverse.

2. homeomorphismnoun

   a similarity in the crystal structure of unrelated compounds

WikipediaRate this definition:0.0 / 0 votes

1. Homeomorphism

   In the mathematical field of topology, a homeomorphism (from Greek ὅμοιος (homoios) 'similar, same', and μορφή (morphē) 'shape, form', named by Henri Poincaré), topological isomorphism, or bicontinuous function is a bijective and 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. 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, such as the deformation of a line into a point. Some homeomorphisms are not continuous deformations, such as the homeomorphism between a trefoil knot and a circle. An often-repeated mathematical joke is that topologists cannot tell the difference between a coffee cup and a 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 the cup's handle.

WikidataRate this definition:0.0 / 0 votes

1. Homeomorphism

   In the mathematical field of topology, a homeomorphism or topological isomorphism or bicontinuous 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 = similar and μορφή = 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 between them.

How to pronounce Homeomorphism?

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How to say Homeomorphism in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of Homeomorphism in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of Homeomorphism in Pythagorean Numerology is: 5

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References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Homeomorphism
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Homeomorphism
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=Homeomorphism