Preservation of uniform continuity under pointwise product

Ahmed Bouziad; Elena Sukhacheva

Preservation of uniform continuity under pointwise product

General Topology 2019-01-17 v1

Authors: Ahmed Bouziad , Elena Sukhacheva

Abstract

Let $X$ be a uniform space and $U(X)$ the linear space of real-valued uniformly continuous functions on $X$ . Our main objective is to give a number of properties characterizing the fact that $U(X)$ is stable under pointwise product in case $X$ is a metric space. Some of these characterizations hold in much more general circumstances.

Keywords

uniform space uniformly continuous functions pointwise product metric space stability

Cite

@article{arxiv.1901.05396,
  title  = {Preservation of uniform continuity under pointwise product},
  author = {Ahmed Bouziad and Elena Sukhacheva},
  journal= {arXiv preprint arXiv:1901.05396},
  year   = {2019}
}

Comments

16 pages, 2 figures; with minor corrections to the published version, mainly in the conclusion of the proof of Proposition 2.1

Preservation of uniform continuity under pointwise product

Abstract

Keywords

Cite

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