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

Result R1869 on D18: Map

Characterisation of equality of maps

Formulation 0

Let $f : X_f \to Y_f$ and $g : X_g \to Y_g$ each be a D18: Map.

Then $f = g$ if and only if

(1)	\begin{equation} X_f = X_g \end{equation}
(2)	\begin{equation} Y_f = Y_g \end{equation}
(3)	\begin{equation} \forall \, x \in X_f : f(x) = g(x) \end{equation}