ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Inverse binary relation
Inverse map
Definition D976
Invertible map
Formulation 1
Let $f : X \to Y$ be a D18: Map.
Then $f$ is an invertible map if and only if there exists a D18: Map $g : Y \to X$ such that
(1) \begin{equation} \forall \, x \in X : g(f(x)) = x \end{equation} (D977: Left-invertible map)
(2) \begin{equation} \forall \, y \in Y : f(g(y)) = x \end{equation} (D978: Right-invertible map)