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

DOI:
https://doi.org/10.1090/S0002-9939-1988-0938652-4

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:
https://doi.org/10.1090/S0002-9939-1988-0938652-4

Keywords:
Small system,
strong small system,
convergence with respect to a small system

Article copyright:
© Copyright 1988
American Mathematical Society