\begin{definition}[Definition:Quasiuniform Space]
Let $\UU$ be a quasiuniformity on a set $S$.
Then a topology $\tau$ can be created from $\UU$ by:
:$\tau := \set {\map u x: u \in \UU, x \in S}$
where:
:$\forall x \in S: \map u x := \set {y: \tuple {x, y} \in u}$
The resulting topological space $T = \struct {S, \tau}$ is called a quasiuniform space.
It can be denoted $\struct {\struct {S, \UU}, \tau}$, or just $\struct {S, \UU}$ if it is understood that $\tau$ is the topology created from $\UU$.
\end{definition}