pre-Urysohn

Definition

A topological space (X, τ) is called pre-Urysohn if for every pair of points x, y ∈ X, there exist U ∈ PO(x), V ∈ PO(y) such that .

Property

• A pre-Urysohn space is pre-T_1.
• A pre-Urysohn space X is Urysohn if and only if it is submaximal.
• A p-regular T_2-space is pre-Urysohn.

Reference

• Paul Ramprasad, Bhattacharyya P., On pre-Urysohn spaces. (English summary), Bull. Malaysian Math. Soc. (2) 22 (1999), no. 1, 23–34.