Regular space

''There are two alternative definitions of the term. Please see:'' Convention:Hausdorffness assumption

Definition
A topological space is said to be regular if it satisfies the following equivalent conditions:

Outside of point-set topology, the term regular space is often used for a regular Hausdorff space, which is the same thing as a regular T1 space. This convention is, however, eschewed by point-set topologists.

Conjunction with other properties

 * Regular Lindelof space: Conjunction with the property of being a Lindelof space.

Textbook references

 * , Page 195, Chapter 4, Section 31 (formal definition, along with normal space)
 * , Page 28 (formal definition)