NET (SEQUENTIAL) CHARACTERIZATION OF EQUICONTINUITY
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Subject Classification General Topology (GT), net convergence, equicontinuous set of functions, neighbourhood, Phrases uniformityAbstract
Net (Sequential) characterization of continuity is almost as old as the subject of General Topology (GT) itself, but no such characterization is known for equicontinuity. This paper furnishes one for equicontinuity. An application when the codomain space is a pseudo- metric space is given.
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References
Gerald B. Folland, REAL ANALYSIS Modern Techniques and their Applications, John Wiley, 1984.
Albert Wilansky, Topology for Analysis, Ginn, 1970.
Sterling K. Berberian, Lectures in Functional Analysis and Operator Theory, GTM 15, Springe-Verlag World Publishing Corporation, Beijin, China 1974.
John Kelly, General Topology, GTM 27, Sspringer-Verlag, New York, 1966.
Karl Stromberg, INTRODUCTION TO CLASSICAL REAL ANALYSIS, Wadsworth International Group 1981.
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