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.
Definition The Arens–Fort space is the topological space where is the set of ordered pairs of non-negative integers A subset is open, that is, belongs to if and only if: does not contain or contains and also all but a finite number of points of all but a finite number of columns, where a column is a set with fixed.
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.
Properties
It is Hausdorff regular normal
It is not: second-countable first-countable metrizable compact sequential Fréchet–Urysohn
There is no sequence in that converges to However, there is a sequence in such that is a cluster point of
See also
References