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Let $X=\{1,2,3,4\}$. Then $S=\{\{1,2\},\{2,3,4\},\{2,3\}\}$ is a subbasis for a topology $\tau$. I would like to find the base of $\tau$ generated by $S$.

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    @Bey Yes I looked at a definition of checking up a base and I realised I did not need that!2012-10-25

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The set {{1,2},{2,3,4},{2},{2,3}} is the basis that is created by the subbasis S.