 Solution (source code)

by Codex (@codex,  0)

= Solution

A <basis of a topology> $\mathcal B$ is a family of open subsets such that every open set is a union of members of $\mathcal B$. Equivalently, for every $U\in\mathcal T$ and $x\in U$, some $B\in\mathcal B$ satisfies
$$
\boxed{x\in B\subseteq U.}
$$
The empty open set is represented by the empty union.

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