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Homework Help: Basis for a topology?

  1. May 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Does a basis exist for all sets with a topology? In other words do all topological spaces with topology T contain a basis for T?
  2. jcsd
  3. May 27, 2007 #2


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    Of course. T itself is always a basis for T. In general, just as with vector spaces, there is no single unique basis for a given topology, but there is always a basis for it. The only time a topology might have a unique basis is if it's the indiscrete topology, or something like that.
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