Definition:Topology Generated by Synthetic Basis

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Definition

Let $S$ be a set.

Let $\mathcal B$ be a synthetic basis of $S$.


Definition 1

The topology on $S$ generated by $\mathcal B$ is defined as:

$\displaystyle \tau = \left\{{\bigcup \mathcal A: \mathcal A \subseteq \mathcal B}\right\}$


Definition 2


Also see