I'm trying to prove the following statement:
Prove that the function f(x)=1/x is continuous on (0,1] but it is not uniformly continuous on this interval.
Thanks a lot.
I actually discuss this in my post here. In essence, (we'll speak less generally now) if (0,1]\to\mathbb{R}" alt="f(0,1]\to\mathbb{R}" /> were uniformly continuous, then we could extend it to some uniformly continuous map . But, this is just nonsense since we'd have to have that