Comparing functional countability and exponential separability
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929515550212096 |
|---|---|
| author | Hernández-Gutiérrez, Rodrigo Spadaro, Santi |
| author_facet | Hernández-Gutiérrez, Rodrigo Spadaro, Santi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparing functional countability and exponential separability Hernández-Gutiérrez, Rodrigo Spadaro, Santi General Topology 54C30, 54F05, 54C35, 54D65 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. |
| title | Comparing functional countability and exponential separability |
| topic | General Topology 54C30, 54F05, 54C35, 54D65 |
| url | https://arxiv.org/abs/2403.15552 |