Frechet-Urysohn property of quasicontinuous functions

2023/02/13 by Alexander V. Osipov, Osipov, Alexander V.
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2302.06437

openalex publication_date 2023/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study the Frechet-Urysohn property of the space Q_p(X,ℝ) of real-valued quasicontinuous functions, defined on a Hausdorff space X, endowed with the pointwise convergence topology. It is proved that under Suslin's Hypothesis, for an open Whyburn space X, the space Q_p(X,ℝ) is Frechet-Urysohn if and only if X is countable. In particular, it is true in the class of first-countable regular spaces X. In ZFC, it is proved that for a metrizable space X, the space Q_p(X,ℝ) is Frechet-Urysohn if and only if X is countable.

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