Uniform convergence spaces

R. Beattie and H.-P. Butzmann
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R. Beattie: Mount Allison University, Department of Mathematics and Computer Science
H.-P. Butzmann: Universität Mannheim, Fakultät für Mathematik und Informatik

Chapter Chapter 2 in Convergence Structures and Applications to Functional Analysis, 2002, pp 59-78 from Springer

Abstract: Abstract Uniform continuity, completeness and equicontinuity are the most important features of uniformities and uniform spaces. Uniform convergence spaces, the convergence generalization of uniform spaces, are not as strong as their topological counterparts. In particular uniform continuity is not a very strong property. But basically all properties of completeness can be carried over to uniform convergence spaces and equicontinuity is an even stronger concept in this more general setting since it is a part of the Arzelà-Ascoli theorem. This theorem, which characterizes relative compactness in function spaces endowed with the continuous convergence structure, has far reaching applications.

Date: 2002
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DOI: 10.1007/978-94-015-9942-9_2

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