Basis for a topology?

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Homework Statement


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?
 

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AKG
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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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