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Homework Help: Topological bases

  1. Sep 12, 2007 #1
    1. The problem statement, all variables and given/known data
    I have seen two definitions for the topology generated by a basis set:
    one here http://books.google.com/books?id=9c...j81v&sig=nNFNyWXorlwCQ8WCwQBDTuI9HUc#PPA22,M1
    and the other one is
    a set U is open if for every x in U, there is a basis element Bi with x in Bi in U

    Are they equivalent?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 12, 2007 #2


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    Science Advisor
    Homework Helper

    Yes. Try proving this yourself and post back if you have problems.
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