Definition:Quasiuniform Space

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Definition

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 $\UU$.


Also see


Sources