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Thread: 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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    Re: Continuity and closure

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