Functionally Hausdorff space

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This is a variation of Hausdorffness. View other variations of Hausdorffness

Definition

A topological space is termed a Urysohn space if for any two points in it, there is a continuous function from the whole space to $[0,1]$ that takes the value $0$ at one point and $1$ at the other.

Relation with other properties

Stronger properties

• Normal space
• Completely regular space

Weaker properties

• Hausdorff space