Does every topological space have a basis for its topology?

pivoxa15 · May 27, 2007

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?

AKG · May 27, 2007

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.

Does every topological space have a basis for its topology?

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Does every topological space have a basis for its topology?

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