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Transactions of the American Mathematical Society

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



The Mackey problem for the compact-open topology

Author: Robert F. Wheeler
Journal: Trans. Amer. Math. Soc. 222 (1976), 255-265
MSC: Primary 46E10
MathSciNet review: 0425593
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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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Keywords: Bounded set, compact-open topology, countably compact, convex strong Mackey property, infrabarrelled space, Mackey space, strict topology, Warner bounded set
Article copyright: © Copyright 1976 American Mathematical Society