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Suppose ( X , δ X ) {\displaystyle (X,\delta _{X})} and ( Y , δ Y ) {\displaystyle (Y,\delta _{Y})} are proximity spaces. A function f : X → Y {\displaystyle f:X\to Y} is termed a proximity map or proximal map if the following is true:
f o r a l l A , B ⊆ Y , f − 1 ( A ) δ X f − 1 ( B ) ⟹ A δ Y B {\displaystyle \ forall\ A,B\subseteq Y,f^{-1}(A)\delta _{X}f^{-1}(B)\implies A\delta _{Y}B} .
