Definition:Uniform Space

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

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

Also see

 * Quasiuniformity Yields a Topology for a proof that $\vartheta$ is actually a topology.