We study the full subcategory A of the category of uniform spaces consisting of those uniform spaces whose set of real-valued uniform maps turns out to be an algebra. The investigation of certain classes of algebras of uniformly continuous functions has been tackled by J. E. Isbell and A. W. Hager. After observing that certain uniform spaces trivially belong to A, such as fine spaces and precompact spaces, we prove that locally fine spaces belong to A. This is a consequence of our main result (Theorem 1.3) which gives a characterization of the objects of A in terms of a particular uniformity on R, precisely the weak uniformity of continuous polynomial dominated functions. Further we discuss some features of the algebras of real valued uniform maps of the objects of A.

Algebras of real valued uniform maps

ARTICO, GIULIANO;MORESCO, ROBERTO
1979

Abstract

We study the full subcategory A of the category of uniform spaces consisting of those uniform spaces whose set of real-valued uniform maps turns out to be an algebra. The investigation of certain classes of algebras of uniformly continuous functions has been tackled by J. E. Isbell and A. W. Hager. After observing that certain uniform spaces trivially belong to A, such as fine spaces and precompact spaces, we prove that locally fine spaces belong to A. This is a consequence of our main result (Theorem 1.3) which gives a characterization of the objects of A in terms of a particular uniformity on R, precisely the weak uniformity of continuous polynomial dominated functions. Further we discuss some features of the algebras of real valued uniform maps of the objects of A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/142568
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