Abstract
A space is functionally countable if every real-valued continuous function has countable image. A stronger property recently defined by Tkachuk is exponential 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 Gδ-topology on exponential separability. Finally, we give some examples of functionally countable spaces that are separable and uncountable.
| Original language | English |
|---|---|
| Article number | 6 |
| Journal | Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |
| Volume | 119 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2025 |
| Externally published | Yes |
Keywords
- 54C30
- 54C35
- 54D65
- 54F05
- Corson compactum
- Eberlein compactum
- Exponentially separable
- Function space
- Functionally countable
- G-topology
- Generalized ordered space
- Ostaszewski space
- Souslin line
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Computational Mathematics
- Applied Mathematics
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