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Math Help - Continuity and closure

  1. #1
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    Continuity and closure

    Hi,
    can anyone help me ?

    Given Topological Spaces (metric spaces) (X, d1) and (Y,d2), show that a function
    f: X -> Y is continuous if and only if f(cl of A) is a subset of cl of f(A) for all A subset X1.
    How can i proof this ?

    Thank you!!!
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  2. #2
    Super Member girdav's Avatar
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    Rouen, France
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    Re: Continuity and closure

    Remember that if f is a function defined on a metric space, then f is continuous if and only if \{f(x_n)\} converges to f(x) whenever \{x_n\} converges to x.
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