Proximity structure induces topology

Statement
Suppose $$(X,\delta)$$ is a fact about::proximity space: $$X$$ is a set and $$\delta$$ is a proximity structure on $$X$$. We can define a natural topology on $$X$$ as follows (thus turning $$X$$ into a fact about::topological space: a subset $$A$$ of $$X$$ is a closed subset if and only if $$\{ x \} \delta A \iff x \in A$$.

Related facts

 * Metric induces proximity structure
 * Metric induces uniform structure
 * Uniform structure induces topology