Definition of homeomorphism in English:


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


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.


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



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.

Definition of homeomorphism in:

Get more from Oxford Dictionaries

Subscribe to remove adverts and access premium resources

Word of the day demoralize
Pronunciation: dɪˈmɒrəlʌɪz
cause (someone) to lose confidence or hope