Pseudocompact sets, absolutely Warner bounded sets and continuous function spaces (Q911000)

Certain topological properties of a completely regular Hausdorff space T characterize functional analytic properties of the locally convex space C(T) of continuous real (complex) valued functions on T under the compact-open topology. Such characterizations have been central in distinguishing closely related properties of locally convex linear topological spaces. The question of such a characterization remains open for the following topological property: Each pseudocompact subset of T is relatively compact. However, this leads naturally to a new topological property characterizing an infrabarrelled type property of C(T). Distinguishing examples and further open questions are included.