Let the plane $\mathbb R \times \mathbb R$, and endow it with the topology generated by the set of complement of 1 lines ( $y= ax+b; a,b\in\mathbb R$ ) . This set is a sub-basis, the question is, found a minimal basis $\mathcal B$, in the sense that given any basis $\mathcal A$ , contained in $\mathcal B$, then $\mathcal A=\mathcal B$.
I conjecture that the basis, is the basis generated by the sub-basis, I´ll like to see other answers to this question