Proximity structure on subspace

Definition
Suppose $$(X,\delta_X)$$ is a proximity space, i.e., $$X$$ is a set and $$\delta_X$$ is a proximity structure on $$X$$. Suppose $$Y \subseteq X$$. The induced proximity structure on $$Y$$, denoted $$\delta_Y$$, is defined as follows:

$$\ \forall \ A,B \subseteq Y, \ A \ \delta_Y \ B \iff A \ \delta_X \ B$$.