Comparing functional countability and exponential separability

2024/03/22 by Hernández-Gutiérrez, Rodrigo, Spadaro, Santi
#54C30 #54C35 #54D65 #54F05 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2403.15552

Abstract

A space is functionally countable if every real-valued continuous function has countable image. A stronger property recently defined by Tkachuk is exponentially separability. We start by studying these properties in GO spaces, where we extend results by Tkachuk and Wilson, and prove a conjecture by Dow. We also study some subspaces of products that are functionally countable and the influence of the G_δ-topology on exponential separability. Finally, we give some examples of functionally countable spaces that are separable and uncountable.

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