ThmDex – An index of mathematical definitions, results, and conjectures.

Result R4543 on D216: Inverse map
Subresult of R4542: Map is inverse to its inverse

Map inverse is invertible

Formulation 0

Let $f : X \to Y$ be a D18: Map such that

(i)	$f^{-1} : Y \to X$ is an D216: Inverse map for $f$

Then $f^{-1}$ is an D976: Invertible map.

Proofs

Proof 0

Let $f : X \to Y$ be a D18: Map such that

(i)	$f^{-1} : Y \to X$ is an D216: Inverse map for $f$

This result is a particular case of R4542: Map is inverse to its inverse. $\square$