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Nearness Convergence

Published online by Cambridge University Press:  20 November 2018

S. A. Naimpally  and
Mohan L. Tikoo
S. A. Naimpally
Affiliation:
Department of Mathematics Kuwait University P.O. Box 5969 SAFAT 130GO KUWAIT
Mohan L. Tikoo
Affiliation:
Department of Mathematic Southeast Missouri State University Cape Girardeau, Missouri 63701 U.S.A.
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Abstract

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In this paper, a concept of nearness convergence is introduced which contains the proximal convergence of Leader as a special case. It is proved that uniform convergence and this nearness convergence are equivalent on totally bounded uniform nearness spaces. One of the features of this convergence is that it lies between uniform convergence and pointwise convergence, and implies uniform convergence on compacta. Some other weaker notions of nearness convergence which are sufficient to preserve nearness maps are also discussed.

Keywords

54D2554E17Convergencenearnessuniformtotally boundedUniform convergenceproximal convergenceDini convergenceArzelà convergenceLeader convergenceUniform convergence on compacta

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 268 - 272
Copyright
Copyright © Canadian Mathematical Society 1990

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