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Proceedings of the American Mathematical Society

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Two function-space topologies

Author: G. A. Edgar
Journal: Proc. Amer. Math. Soc. 39 (1973), 219-220
MSC: Primary 46E10
MathSciNet review: 0313771
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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 [Enhancements On Off] (What's this?)

  • [1] 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 Sci. Ind., no. 1189, Herman & Cie, Paris, 1953 (French). MR 0054161
  • [2] -, Éléments de mathématique. Fasc. XIII. Livre VI: Intégration, Actualités Sci. Indust., no. 1175, Hermann, Paris, 1952. MR 14, 960.
  • [2a] -, Ibid., 2nd ed., 1965. MR 36 #2763.
  • [3] G. Choquet, Lectures in analysis. Vol. I, Benjamin, New York, 1969. MR 40 #3252.

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Keywords: Locally convex topology, inductive limit topological vector space, compactly supported function, Radon measure, Lebesgue integral
Article copyright: © Copyright 1973 American Mathematical Society