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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

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    I can't make any sense out of this question.2011-08-17
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    @Alexei: I take Daniel to be asking the following question. Let $\mathscr{S}$ be the set of complements of straight lines in the plane, and take $\mathscr{S}$ as the subbase for a topology $\mathscr{T}$. Let $\mathscr{B}$ be the set of finite intersections of members of $\mathscr{S}$. If $\mathscr{B_1}$ is a minimal base for $\mathscr{T}$ with respect to inclusion, is it true that $\mathscr{B_1}=\mathscr{B}$?2011-08-17
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    that is the question, find a minimal basis2011-08-17
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    So what did you try, Daniel?2011-08-17

2 Answers 2