Definition of homeomorphism in English:

homeomorphism

nounˌhəʊmɪə(ʊ)ˈmɔːfɪz(ə)mˌhɒmɪə(ʊ)ˈmɔːfɪz(ə)mˌhoʊmiəˈmɔrˌfɪzəm

Mathematics

An instance of topological equivalence.
〔数〕同胚，同拓扑
Example sentencesExamples
- In topology, the most basic equivalence is a homeomorphism, which allows spaces that appear quite different in most other subjects to be declared equivalent in topology.
- We prove that it is not possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the circle to a quasiconformal homeomorphism of the disk.

Derivatives

homeomorphic

adjectivehɒmɪəˈmɔːfɪkhəʊmɪəˈmɔːfɪkˌhoʊmiəˈmɔrfɪk

Mathematics

Without such a reference space we can only say whether our strips are homeomorphic or not, which they indeed are whenever they differ in an even number of twists.
Example sentencesExamples
- We now consider objects that are homeomorphic to the unit circle.
- The most important result in this paper is that two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic.
- His paper to the International Mathematical Congress in Cambridge in England in 1912 was of major importance for it sketched the definition of a curve without arcs, so that it had no homeomorphic images of a segment of a straight line.

Origin

From Greek homoios 'like' + morphē 'form' + -ism.

Definition of homeomorphism in US English:

homeomorphism

nounˌhōmēəˈmôrˌfizəmˌhoʊmiəˈmɔrˌfɪzəm

Mathematics

An instance of topological equivalence to another space or figure.
〔数〕同胚，同拓扑
Example sentencesExamples
- In topology, the most basic equivalence is a homeomorphism, which allows spaces that appear quite different in most other subjects to be declared equivalent in topology.
- We prove that it is not possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the circle to a quasiconformal homeomorphism of the disk.

Origin

From Greek homoios ‘like’ + morphē ‘form’ + -ism.

词汇	homeomorphism
释义	Definition of homeomorphism in English: homeomorphism nounˌhəʊmɪə(ʊ)ˈmɔːfɪz(ə)mˌhɒmɪə(ʊ)ˈmɔːfɪz(ə)mˌhoʊmiəˈmɔrˌfɪzəm Mathematics An instance of topological equivalence. 〔数〕同胚，同拓扑 Example sentencesExamples In topology, the most basic equivalence is a homeomorphism, which allows spaces that appear quite different in most other subjects to be declared equivalent in topology. We prove that it is not possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the circle to a quasiconformal homeomorphism of the disk. Derivatives homeomorphic adjectivehɒmɪəˈmɔːfɪkhəʊmɪəˈmɔːfɪkˌhoʊmiəˈmɔrfɪk Mathematics Without such a reference space we can only say whether our strips are homeomorphic or not, which they indeed are whenever they differ in an even number of twists. Example sentencesExamples We now consider objects that are homeomorphic to the unit circle. The most important result in this paper is that two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic. His paper to the International Mathematical Congress in Cambridge in England in 1912 was of major importance for it sketched the definition of a curve without arcs, so that it had no homeomorphic images of a segment of a straight line. Origin From Greek homoios 'like' + morphē 'form' + -ism. Definition of homeomorphism in US English: homeomorphism nounˌhōmēəˈmôrˌfizəmˌhoʊmiəˈmɔrˌfɪzəm Mathematics An instance of topological equivalence to another space or figure. 〔数〕同胚，同拓扑 Example sentencesExamples In topology, the most basic equivalence is a homeomorphism, which allows spaces that appear quite different in most other subjects to be declared equivalent in topology. We prove that it is not possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the circle to a quasiconformal homeomorphism of the disk. Origin From Greek homoios ‘like’ + morphē ‘form’ + -ism.
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