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Here's a problem that I'm having trouble with:

Give an example of metric spaces X and Y and continuous maps f: X->Y and g: Y->X such that f and g are both bijective but X and Y are not homeomorphic.

I can find plenty of examples where I can find one such function, but finding the second is always a problem.

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# Homework Help: Topology question; examples of non-homeomorphic metric spaces

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