# Thread: Show that f is bounded.

1. ## Show that f is bounded.

Suppose f: K-> (-$\displaystyle \infty$,$\displaystyle \infty$), 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 {$\displaystyle G_alpha$} 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?

2. Originally Posted by alice8675309
Suppose f: K-> (-$\displaystyle \infty$,$\displaystyle \infty$), 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 {$\displaystyle G_alpha$} 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?

3. 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.

4. Originally Posted by Drexel28
Yeah, we'll use it. How though?
I don't think I'm fully understanding this

5. 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.