Proximity map

Definition
Suppose $$(X,\delta_X)$$ and $$(Y,\delta_Y)$$ are defining ingredient::proximity spaces. A function $$f:X \to Y$$ is termed a proximity map or proximal map if the following is true:

$$ \ forall \ A,B \subseteq Y, f^{-1}(A) \delta_X f^{-1}(B) \implies A \delta_Y B$$.