Some properties involving feeble compactness, II: Generalized Σ-products and Cp-spaces

Abstract

In [14], we begin analyzing some classes of topological spaces contained in the class of feebly compact spaces. In this article, which is a second part of that work, we determine, for a compact metrizable topological group G, when Cp(X,G) is selectively pseudocompact, and when it is weakly compact-bounded for a Tychonoff space X. Moreover, we prove that for some Hausdorff extensions XQ of a space X constructed using free filters on X, the space Cp(XQ,G) is selectively sequentially pseudocompact. We therefore obtain a class of spaces having sufficient conditions to affirmatively solve Problem 8.5 posed by Dorantes-Aldama and Shakmatov in [7].