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In page 299 of Ravi Vakil's lecture "Foundations of algebraic geometry" , there is a statement: For a scheme X, the category of affine open sets, and distinguished inclusions, forms a filtered set. Given two affine open sets U and V of the scheme X, if the intersection of U and V is empty, how can we find an upper bound of U and V ?

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    Is the union of the $U,V$ off the mark here? A lower bound would be the open set. Am I missing something?2011-07-18
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    Could you please give a reference in terms of sections rather than pages, because of the changes due to successive online versions ?2011-07-18
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    it is section 14.3.1. I think that the affine open sets containing a fixed point, and distinguished inclusions, form a filtered set, not for all affine open sets and distinguished inclusions.2011-07-18

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