Preservation of uniform continuity under pointwise product

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.

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