- #1
jRSC
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Hey guys, I'm reading Munkres book (2nd edition) and am caught on a problem out of Ch. 2. The problem states:
If {Ta} is a family of topologies on X, show that (intersection)Ta is a topology on X. Is UTa 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}, T1={{a}}, and T2={{b}}, then T1UT2={{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.
If {Ta} is a family of topologies on X, show that (intersection)Ta is a topology on X. Is UTa 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}, T1={{a}}, and T2={{b}}, then T1UT2={{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.