The uniform convergence topology on separable subsets
Journal
Topology and its Applications
ISSN
0166-8641
Publisher
Eslevier
Date Issued
2025
Author(s)
Cruz-Chapital, Jorge Antonio
Rojas-Sánchez, Alejandro Darío
Tamariz-Mascarúa, Ángel
Villegas-Rodríguez, Humberto
Type
text::journal::journal article
Abstract
For a topological space X, let be the cartesian product of copies of the real line with the topology of the uniform convergence on separable subsets of X. In this article we analyze the subspace of of all real-valued continuous functions on X, denoted by. We determine when is dense and when is closed in, and we obtain some results about the Baire property in. Finally, we determine the cellularity of where is the space of ordinal numbers belonging to with its usual order topology. ©The authors ©Topology and its Applications ©Elsevier.
License
Acceso Restringido
How to cite
Cruz-Chapital, J. A., Rojas-Sánchez, A. D., Tamariz-Mascarúa, Á., & Villegas-Rodríguez, H. (2025). The uniform convergence topology on separable subsets. Topology and Its Applications, 359, 109135. https://doi.org/10.1016/j.topol.2024.109135