MathGloss

The topology generated by a basis $\mathcal B$ is the collection $\tau$ of subsets $U$ such that for every such that for every $x\in U$, there exists a $B\in \mathcal B$ such that $x\in B\subset U$.

Equivalently, $U\in \tau$ if and only if it is a union of sets in $\beta$.

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