Locally uniformly continuous functions
Author: Alexander J. Izzo
Journal: Proc. Amer. Math. Soc. 122 (1994), 1095-1100
MSC: Primary 54C30; Secondary 46B45, 54C05, 54E50
MathSciNet review: 1216816
Abstract: It is shown that on every infinite-dimensional separable normed space there exist continuous real-valued functions that are nowhere locally uniformly continuous. An explicit example of such a function on is given. It is also shown that every continuous real-valued function on a metric space can be approximated uniformly by locally uniformly continuous functions.