Hey guys, I'm reading Munkres book (2nd edition) and am caught on a problem out of Ch. 2. The problem states:(adsbygoogle = window.adsbygoogle || []).push({});

If {T_{a}} is a family of topologies on X, show that (intersection)T_{a}is a topology on X. Is UT_{a}a topology on X?

Sorry for crappy notation; I don't know my way around the symbols yet.

For the latter, I say "not necessarily"; for example, if X={a,b,c}, T_{1}={{a}}, and T_{2}={{b}}, then T_{1}UT_{2}={{a},{b}} is not a topology on X because {a,b} is not in the union. If this is wrong, please correct me. However, I am having a very difficult time with these proofs; for the former part of the question, I know the intersection will yield a "coarsest" subset of X, but proving it is a topology is bewildering me.

Thanx for any help.

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# Simple Topology problem (Munkres)

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