Proximity structure induces topology

Statement

Suppose $(X,\delta )$ is a 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 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