Arens-Fort space

In mathematics, the Arens-Fort space is a special example in the theory of topological spaces, named for Richard Friederich Arens and M. K. Fort, Jr.

Let "X" be a set of ordered pairs of non-negative integers (m,n). A subset "U" of "X" is open if and only if:
*it does not contain (0,0), or
*it contains (0,0), and all but a finite number of points in all but a finite number of columns, where a column is a set {(m,n)} with fixed m.

In other words, an open set is only "allowed" to contain (0,0) if only a finite number of its columns contain significant gaps. By a significant gap in a column we mean the omission of an infinite number of points.

It is
* Hausdorff
* regular
* normal

It is not:
* second-countable
* first-countable
* metrizable
* compact

ee also

* Fort space

References

* | year=1995