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Math Help - showing continuity of of limit function

  1. #1
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    showing continuity of of limit function

    Let X be a topological space and A, a dense subset. Let f: A-->Y be a continuous function where Y is regular. Further assume that for x in A, if lim x = y then lim f(x) exists. Now define a function g: X-->Y by defining g(y) = lim f(x) as x-->y . Show that g is continuous on X.


    This question has me stumped. I'd appreciate any help on this.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by guroten View Post
    Let X be a topological space and A, a dense subset. Let f: A-->Y be a continuous function where Y is regular. Further assume that for x in A, if lim x = y then lim f(x) exists. Now define a function g: X-->Y by defining g(y) = lim f(x) as x-->y . Show that g is continuous on X.


    This question has me stumped. I'd appreciate any help on this.
    Are these filters, or seuqneces?
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  3. #3
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    They are sequences.
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