ThmDex – An index of mathematical definitions, results, and conjectures.
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Constant map
Definition D3966
Constancy-preserving map
Formulation 0
Let $f : X \to Y$ and $g : X \to Z$ each be a D18: Map.
Then $f$ constancy-preserving with respect to $g : X \to Z$ if and only if \begin{equation} \forall \, x, y \in X \left( g(x) = g(y) \quad \implies \quad f(x) = f(y) \right) \end{equation}