# Regular Space

In topology and related fields of mathematics, a topological space X is called a regular space if every non-empty closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods. Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These conditions are examples of separation axioms.

Read more about Regular Space:  Definitions, Relationships To Other Separation Axioms, Examples and Nonexamples, Elementary Properties

### Other articles related to "space, regular, regular space, regular spaces":

Tychonoff Space - Examples and Counterexamples
... Almost every topological space studied in mathematical analysis is Tychonoff, or at least completely regular ... Other examples include Every metric space is Tychonoff every pseudometric space is completely regular ... Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff ...
Regular Space - Elementary Properties
... Suppose that X is a regular space ... In fact, this property characterises regular spaces if the closed neighbourhoods of each point in a topological space form a local base at that point, then the space ... these closed neighbourhoods, we see that the regular open sets form a base for the open sets of the regular space X ...
Glossary Of Topology - R
... Regular A space is regular if, whenever C is a closed set and x is a point not in C, then C and x have disjoint neighbourhoods ... Regular Hausdorff A space is regular Hausdorff (or T3) if it is a regular T0 space ... A regular space is Hausdorff if and only if it is T0, so the terminology is consistent.) Regular open An open subset U of a space X is regular open if it equals the interior of its ...

### Famous quotes containing the words space and/or regular:

Art and power will go on as they have done,—will make day out of night, time out of space, and space out of time.
Ralph Waldo Emerson (1803–1882)

My attitude toward punctuation is that it ought to be as conventional as possible. The game of golf would lose a good deal if croquet mallets and billiard cues were allowed on the putting green. You ought to be able to show that you can do it a good deal better than anyone else with the regular tools before you have a license to bring in your own improvements.
Ernest Hemingway (1899–1961)