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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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Two function-space topologies
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by G. A. Edgar PDF
Proc. Amer. Math. Soc. 39 (1973), 219-220 Request permission

Abstract:

Two topologies for the set of all continuous functions with compact support are shown to be distinct. One of the topologies is the usual inductive limit topology, and the other is a topology claimed by G. Choquet to coincide with it.
References
  • N. Bourbaki, Eléments de mathématique. XV. Première partie: Les structures fondamentales de l’analyse. Livre V: Espaces vectoriels topologiques. Chapitre I: Espaces vectoriels topologiques sur un corps valué. Chapitre II: Ensembles convexes et espaces localement convexes, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1189, Hermann & Cie, Paris, 1953 (French). MR 0054161
  • —, Éléments de mathématique. Fasc. XIII. Livre VI: Intégration, Actualités Sci. Indust., no. 1175, Hermann, Paris, 1952. MR 14, 960. —, Ibid., 2nd ed., 1965. MR 36 #2763. G. Choquet, Lectures in analysis. Vol. I, Benjamin, New York, 1969. MR 40 #3252.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 219-220
  • MSC: Primary 46E10
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0313771-3
  • MathSciNet review: 0313771