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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Weak topologies and equicontinuity


Authors: Donald F. Reynolds and John W. Schleusner
Journal: Proc. Amer. Math. Soc. 80 (1980), 349-352
MSC: Primary 54C30
MathSciNet review: 577772
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Abstract: Corresponding to each family F of real-valued functions on a set X, there is a weakest topology on X for which F is equicontinuous. This equiweak topology is pseudometrizable and provides a characterization of metrizable topologies in terms of point-separating families of real-valued functions.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0577772-6
Keywords: Equicontinuity, weak topologies, metrization
Article copyright: © Copyright 1980 American Mathematical Society