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Math Help - Show that f is bounded.

  1. #1
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    Show that f is bounded.

    Suppose f: K-> (- \infty, \infty), K is compact, and f has a finite limit at each point of K, but may not be continuous on K. Show that f is bounded by using the definition of compactness in terms of open covers.

    I think this is the def. I'm supposed to be using. A set E is compact iff, for every family { G_alpha} for some alpha in A of open sets such that EC alpha in A G_alpha, there is a finite set {alpha1,...,alphan} C A such that ECUi=1 to infinity G_(alphai).

    Also, how would we show it if we use the sequential characterization of compactness?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by alice8675309 View Post
    Suppose f: K-> (- \infty, \infty), K is compact, and f has a finite limit at each point of K, but may not be continuous on K. Show that f is bounded by using the definition of compactness in terms of open covers.

    I think this is the def. I'm supposed to be using. A set E is compact iff, for every family { G_alpha} for some alpha in A of open sets such that EC alpha in A G_alpha, there is a finite set {alpha1,...,alphan} C A such that ECUi=1 to infinity G_(alphai).

    Also, how would we show it if we use the sequential characterization of compactness?
    Yeah, we'll use it. How though?
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  3. #3
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    Thats what im not sure of lol because I keep going back to the fact that since K is compact then it is closed and bounded.
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    Quote Originally Posted by Drexel28 View Post
    Yeah, we'll use it. How though?
    I don't think I'm fully understanding this
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  5. #5
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    hm, does anyone know how to do this problem? I don't understand that def either, and I'm pretty sure I've come acrossed it in my book as well.
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