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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Mackey problem for the compact-open topology
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by Robert F. Wheeler PDF
Trans. Amer. Math. Soc. 222 (1976), 255-265 Request permission

Abstract:

Let ${C_c}(T)$ denote the space of continuous real-valued functions on a completely regular Hausdorff space T, endowed with the compact-open topology. Well-known results of Nachbin, Shirota, and Warner characterize those T for which ${C_c}(T)$ is bornological, barrelled, and infrabarrelled. In this paper the question of when ${C_c}(T)$ is a Mackey space is examined. A convex strong Mackey property (CSMP), intermediate between infrabarrelled and Mackey, is introduced, and for several classes of spaces (including first countable and scattered spaces), a necessary and sufficient condition on T for ${C_c}(T)$ to have CSMP is obtained.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 222 (1976), 255-265
  • MSC: Primary 46E10
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0425593-0
  • MathSciNet review: 0425593