Urysohn

Definition

• A topological space (X, τ) is said to be a Urysohn space if every pair of distinct points have disjoint closed neighbourhoods.

Property

• Urysohn ⇒ strongly Hausdorff.
• Urysohn ⇒ pre-Urysohn. [2]

Reference

1. Porter, J. R., Strongly Hausdorff spaces. Acta Math. Acad. Sci. Hungar. 25 (1974), 245–248.
2. Paul Ramprasad, Bhattacharyya P., On pre-Urysohn spaces. (English summary), Bull. Malaysian Math. Soc. (2) 22 (1999), no. 1, 23–34.