Definition:Uniform Space

Definition
Let $\mathcal U$ be a uniformity on a set $S$.

The quasiuniform space $\left({\left({S, \mathcal U}\right), \tau}\right)$ generated from $\mathcal U$ is a uniform space.

Also see

 * Quasiuniformity Induces Topology for a proof that $\tau$ is actually a topology.