bijection

Noun

Meaning

bijection (plural bijections)

(set theory) A one-to-one correspondence, a function which is both a surjection and an injection.

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Examples

A homeomorphism is a bijection that is continuous and whose inverse is also continuous. Source: Internet

A function is invertible if and only if it is a bijection. Source: Internet

And in fact, Cantor's diagonal argument is constructive, in the sense that given a bijection between the real numbers and natural numbers, one constructs a real number that doesn't fit, and thereby proves a contradiction. Source: Internet

Any surjective function induces a bijection defined on a quotient of its domain by collapsing all arguments mapping to a given fixed image. Source: Internet

Definition Given two manifolds M and N, a differentiable map f : M → N is called a diffeomorphism if it is a bijection and its inverse f −1 : N → M is differentiable as well. Source: Internet

Cardinality of infinite sets main Two sets are said to have the same cardinality or cardinal number if there exists a bijection (a one-to-one correspondence) between them. Source: Internet

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