in the munkres book, they define A to be a subbasis of X if it is a collection of subsets of X whose union equals X. They define T, the topology generated by the subbasis to be the collection of all unions of finite intersections of elements of A.(adsbygoogle = window.adsbygoogle || []).push({});

This definition seems to be flawed because, given that definition, i can easily construct a set A that is a subbasis but wont generate a topology. For example, given any set X let A be a partition on X (A is made of disjoint sets). Any finite intersection here would be empty and therefore T (the topology generated by A) would be empty. I think the only way to resolve this issue is to add that X must be an element of A.

I think they assume this but it just bothers me that they didnt write it down explicitly.

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# Another topology question

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