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

Definition of homeomorphism in English:


An instance of topological equivalence.
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.


Pronunciation: /hɒmɪəˈmɔːfɪk/
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.


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

Definition of homeomorphism in:
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