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 where is the set of ordered pairs of non-negative integers A subset 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 that converges to However, there is a sequence in such that is a cluster point of
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 where is the set of ordered pairs of non-negative integers A subset 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 that converges to However, there is a sequence in such that is a cluster point of