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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.

References [Enhancements On Off] (What's this?)

  • [1] J. A. Guthrie and M. Henry, Metrization, paracompactness, and real-valued functions, Fund. Math. 95 (1977), 49-54. MR 0436090 (55:9041)
  • [2] -, Metrization, paracompactness, and real-valued functions. II, Fund. Math. 104 (1979), 13-20. MR 549377 (81c:54018)

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Keywords: Equicontinuity, weak topologies, metrization
Article copyright: © Copyright 1980 American Mathematical Society

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