The Mackey problem for the compact-open topology

Author:

Wheeler Robert F.

Abstract

Let C c ( T ) {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 ) {C_c}(T) is bornological, barrelled, and infrabarrelled. In this paper the question of when C c ( T ) {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 ) {C_c}(T) to have CSMP is obtained.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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