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Math Help - Continuous functions in a metric space problem...

  1. #1
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    Continuous functions in a metric space problem...

    With the following problem, would I do it by showing the the complement is open or by showing that it contains all it's limit points (or something else - if so, what)? I can't see in what way I would use either method.


    Let (X,d) and (Y,e) be metric spaces, let f,g:X to Y be continuous. Prove that the set B = {x in X : f(x) = g(x)} is a closed subset of X.
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  2. #2
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    I would show that the set contains all of its limit points.
    If p is a limit point of the set then there is a sequence of points in B and \left( {x_n } \right) \to p.

    Well what do you know about f\left( {x_n } \right) and about g\left( {x_n } \right)?
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