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 T _{3}**. The term "

**T**" usually means "a regular Hausdorff space". These conditions are examples of separation axioms.

_{3}spaceRead 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":

... 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 ...

...

**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)