Completeness properties of the pseudocompact-open topology on C(X)

Abstract

ABSTRACT. This is a study of the completeness properties of the space C ps (X) of continuous real-valued functions on a Tychonoff space X, where the function space has the pseudocompact-open topology. The properties range from complete metrizability to the Baire space property.

QC(X) Üzerinde Yarı Kompakt-Açık Topoloji

“…Bazılarını -kompakt-açık (Gulick, 1992), sözde kompakt-açık (Kundu and Garg, 2016), C-kompakt-açık (Osipov, 2012), sınırlı-açık (Kundu and Raha, 1995) ve açık-açık topoloji (Porter,1993) Ģeklinde sıralanabilir.…”

On sequentially compact-open topology

“…[2]). Пусть F = {a} ∪ A, где A несчётное дискретное подпространство, а окрестностями точки a являются множества вида {a} ∪ (A \ C), где C ⊂ A и C счётно.…”

The dual of Cps(X)

“…This topology has already been well-studied in [19], [20] and [18]. In particular, in these papers, the submetrizability, metrizability, completeness and countability properties of the pseudocompact-open topology on C(X) have been studied.…”