Weak topologies and equicontinuity

Reynolds, Donald F.; Schleusner, John W.

doi:10.1090/S0002-9939-1980-0577772-6

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weak topologies and equicontinuity
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by Donald F. Reynolds and John W. Schleusner PDF

Proc. Amer. Math. Soc. 80 (1980), 349-352 Request permission

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.

References

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J. A. Guthrie and Michael Henry, Metrization, paracompactness, and real-valued functions. II, Fund. Math. 104 (1979), no. 1, 13–20. MR 549377, DOI 10.4064/fm-104-1-13-20