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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Small systems convergence and metrizability


Authors: Roy A. Johnson, Jerzy Niewiarowski and Tadeusz Świątkowski
Journal: Proc. Amer. Math. Soc. 103 (1988), 105-112
MSC: Primary 28A20; Secondary 54A20
MathSciNet review: 938652
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Abstract: The abstract notion of convergence of functions with respect to a small system has its roots in the concept of convergence of functions in measure. The second author has shown that convergence of functions with respect to a small system generates a Fréchet topology. In this paper we show that convergence with respect to a small system is equivalent to convergence with respect to a certain complete pseudometric (or metric if we consider equivalence classes of functions with respect to the small system).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938652-4
PII: S 0002-9939(1988)0938652-4
Keywords: Small system, strong small system, convergence with respect to a small system
Article copyright: © Copyright 1988 American Mathematical Society