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 defining ingredient::Hausdorff space.
 * 2) It is both a regular space and a defining ingredient::T1 space.
 * 3) It is both a regular space and a defining ingredient::Kolmogorov space (i.e., a $$T_0$$ 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.