Show that the function defined by is not uniformly continuous. I want to show this using the following corollary: Let be a subset of , let be a uniformly continuous function, and let be an adherent point of . Then exists and is a real number.

So is an adherent point of , because contains a point of for every (its probably assumed that ). And does not exist, which implies that is not uniformly continuous. I used the contrapositive of the corollary.

Is this correct?