Definition:Basis (Topology)/Analytic Basis/Definition 2

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Definition

Let $\left({S, \tau}\right)$ be a topological space.

Let $\mathcal B \subseteq \tau$.


Then $\mathcal B$ is an analytic basis for $\tau$ if and only if:

$\forall U \in \tau: \forall x \in U: \exists V \in \mathcal B: x \in V \subseteq U$


Also see

  • Results about analytic bases can be found here.


Sources