1. The problem statement, all variables and given/known data Show that if a function f:(0,1) --> lR is uniformly continuous, f is bounded. 2. Relevant equations - 3. 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.