Definition of homeomorphism in English:

homeomorphism

Line breaks: homeo|morph|ism
Pronunciation: /ˌhɒmɪə(ʊ)ˈmɔːfɪz(ə)m
 
, ˌhəʊm-/

noun

Mathematics
  • An instance of topological equivalence.
    More example sentences
    • 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

adjective
More example sentences
  • 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.
  • The most important result in this paper is that two real algebraic manifolds are equivalent if and only if they are analytically homeomorphic.
  • 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.

Origin

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

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