Is Uniform Continuity a Property of Bounded Functions?

[3605]

Homework Statement

Show that if a function f:(0,1) --> lR is uniformly continuous, f is bounded.

Homework Equations

-

The Attempt at a Solution

Really don´t know. I started thinking about Weierstrass Thereom but I am not sure that it´s ok. Now I think that may be is something about the properties of uniform continuities. Any help would be great.

Thanks in advance.

 

[morphism]

This is an easy epsilon-delta argument. Work with the definition of uniform continuity. (It's always helpful to draw a picture.)