# Find a function f: D-> R such that f is continuous but not uniformly continuous

• April 18th 2011, 07:38 AM
alice8675309
Find a function f: D-> R such that f is continuous but not uniformly continuous
Let p $\in$[0,1] and D=[0,1]-{p}. find a function f: D->R such that f is continuous at every point of D but is not uniformly continuous on D.

Would 1/x work for this as well but how do I prove it?
• April 18th 2011, 07:52 AM
FernandoRevilla
• April 18th 2011, 08:13 AM
alice8675309
Quote:

Originally Posted by FernandoRevilla

yes this is my other post. However i started a new thread with new conditions so it didn't get confusing. At first I thought x^2 would work as well but then based on the other post I thought it would be 1/x but i dont know how to prove it and I didn't think it could be proved the same way as the other post because there are new conditions.
• April 18th 2011, 08:19 AM
FernandoRevilla
Quote:

Originally Posted by alice8675309
yes this is my other post. However i started a new thread with new conditions so it didn't get confusing. At first I thought x^2 would work as well but then based on the other post I thought it would be 1/x but i dont know how to prove it and I didn't think it could be proved the same way as the other post because there are new conditions.

You only need to choose p = 0 .