Regular Hausdorff space

Definition

A topological space is termed a regular Hausdorff space or a $T_{3}$ space if it satisfies the following equivalent conditions:

1. It is both a regular space and a Hausdorff space.
2. It is both a regular space and a T1 space.

Note that outside of point-set topology, and in many elementary treatments, the term regular space is used to stand for regular 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

In the T family (properties of topological spaces related to separation axioms), this is called: T3