Editing Regular space (section)

{{Short description|Property of topological space}}
{{More citations needed|date=April 2022}}
{{Separation axioms}}

In [[topology]] and related fields of [[mathematics]], a [[topological space]] ''X'' is called a '''regular space''' if every [[closed subset]] ''C'' of ''X'' and a point ''p'' not contained in ''C'' have non-overlapping [[open neighborhood]]s.<ref>{{cite book | last=Munkres | first=James R. | authorlink=James Munkres | title=Topology | edition=2nd | publisher=[[Prentice Hall]] | year=2000 | isbn=0-13-181629-2}}</ref> Thus ''p'' and ''C'' can be [[separated sets|separated]] by neighborhoods. This condition is known as '''Axiom T<sub>3</sub>'''. The term "'''T<sub>3</sub> space'''" usually means "a regular [[Hausdorff space]]". These conditions are examples of [[separation axiom]]s.