different between bijection vs homeomorphism

English

Etymology

From French bijection, introduced by Nicolas Bourbaki in their treatise Éléments de mathématique.

Pronunciation

• IPA^(key): /ba?.d??k.??n/

Noun

bijection (plural bijections)

1. (set theory) A one-to-one correspondence, a function which is both a surjection and an injection.
   • 2002, Yves Nievergelt, Foundations of Logic and Mathematics, page 214,

     The present text has defined a set to be finite if and only if there exists a bijection onto a natural number, and infinite if and only if there does not exist any such bijection.

   • 2007, C. J. Date, Logic and Databases: The Roots of Relational Theory, page 167,

     Note in particular that a function is a bijection if and only if it's both an injection and a surjection.

   • 2013, William F. Basener, Topology and Its Applications, unnumbered page,

     The basic idea is that two sets A and B have the same cardinality if there is a bijection from A to B. Since the domain and range of the bijection is not relevant here, we often refer to a bijection from A to B as a bijection between the sets, or a one-to-one correspondence between the elements of the sets.

Synonyms

• (function that is both a surjection and an injection): one-to-one correspondence

Related terms

• injection
• surjection

Translations

Anagrams

• objicient

French

Pronunciation

• IPA^(key): /bi.??k.sj??/

Noun

bijection f (plural bijections)

1. (set theory) bijection

English

Alternative forms

• homoeomorphism (UK)
• homœomorphism

Etymology

homeo- +? -morphism

Noun

homeomorphism (plural homeomorphisms)

1. (topology) a continuous bijection from one topological space to another, with continuous inverse.
2. (chemistry) a similarity in the crystal structure of unrelated compounds

Hypernyms

• (topology): equivalence relation

Translations

See also

• homeomorphism on Wikipedia.Wikipedia
• diffeomorphism