Problem sheet #1 correction question 2 (update 21/10)

It was kindly pointed out to me that in question 2 the sensitivity constant cannot always be choses any number smaller rather than the diameter. But it can always be chosen to be anything smaller than 1/2 the diameter. I have amended the question on the problem sheet and model answer, accordingly. [I took the erroneous question from [HK] exercise 7.2.3.] While correct, half the diameter is not always optimal. Namely, if X is compact, the sensitivity constant can be chosen to be any number smaller than $\inf_{x\in X}(\sup_{y\in X} d(x,y))$. I included the argument with the model answer. This quantity can be equal to the diameter; eg on $S^1$.