Year: 2026
Type: preprint
Abstract: In this paper we prove that $B_1(X)$ has a dense cofinally Polish subspace if and only if $X$ is a $Δ_1$-space. Also we prove that $B_1(X, [0,1])$ has a dense cofinally Polish subspace if and only if $X$ is a weak $λ$-space. We also establish that $C_p(X, [0,1])$ is pseudocompact if and only if $C_p(X,[0,1])$ has a dense cofinally Polish subspace. This result provides answers to four open questions from (Tkachuk in RACSAM 115(68), 2021).
Source: arXiv (Cornell University)
Author: Osipov, Alexander V.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220659017