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What is an underlying topological space?

I don't get the definition of this in my topology book.

I wonder what the definition of an underlying topological space is.

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You’ll have to give more context: you haven’t given enough information for the question to be answered. – Brian M. Scott Oct 24 '12 at 12:59

If you're dealing with a topological {group, vector space, ring or any other algebraic structure}, referring to "the underlying topological space" usually means to look at the object only as a topological space.

You can find this with Lie groups, the real spaces $\,\Bbb R^n\,$, general Hilbert or Banach spaces, etc.

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