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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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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 $ {l^p}\;(1 \leq p < \infty )$ 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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1216816-5
PII: S 0002-9939(1994)1216816-5
Article copyright: © Copyright 1994 American Mathematical Society