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.

The Arens–Fort space is the topological space

is the set of ordered pairs of non-negative integers

is open, that is, belongs to

if and only if: In other words, an open set is only "allowed" to contain

if only a finite number of its columns contain significant gaps, where a gap in a column is significant if it omits an infinite number of points.

It is It is not: There is no sequence in

However, there is a sequence

is a cluster point of