Small systems convergence and metrizability

Johnson, Roy A.; Niewiarowski, Jerzy; Świątkowski, Tadeusz

doi:10.1090/S0002-9939-1988-0938652-4

Small systems convergence and metrizability
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by Roy A. Johnson, Jerzy Niewiarowski and Tadeusz Świątkowski PDF

Proc. Amer. Math. Soc. 103 (1988), 105-112 Request permission

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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