Relativized Urysohn Spaces - May-Custodio, Victor Gustavo; Ramírez-Páramo, Alejandro (Topology Proceedings, 2021)
In this paper, we introduce relative formulations of the Urysohn separation axiom. We prove some versions of classical results regarding Urysohn spaces that are formulated in terms of the relative concepts of the Urysohn axiom, and some lead to results in the absolute notion. We discuss the classical relation between distinct separation axioms. Finally, we obtain cardinal inequalities which boil down to results in the absolute case of a Urysohn space.