Definition:Basis (Topology)/Analytic Basis/Definition 1

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Definition

Let $\struct {S, \tau}$ be a topological space.


An analytic basis for $\tau$ is a subset $\BB \subseteq \tau$ such that:

$\displaystyle \forall U \in \tau: \exists \AA \subseteq \BB: U = \bigcup \AA$


That is, such that for all $U \in \tau$, $U$ is a union of sets from $\BB$.


Also see

  • Results about analytic bases can be found here.


Sources