Definition:Topology Generated by Synthetic Basis/Definition 3
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Definition
Let $S$ be a set.
Let $\BB$ be a synthetic basis of $S$.
The topology on $S$ generated by $\BB$ is defined as:
- $\tau = \set {U \subseteq S: \forall x \in U: \exists B \in \BB: x \in B \subseteq U}$