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 . A subset U of X is open 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. By a significant gap in a column we mean the omission of an infinite number of points.
It is
It is not: