Arens–Fort space | Wikipedia audio article
Channel: Subhajit Sahu
Date: 29/03/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Arens%E2%80%93Fort_space


00:01:11 See also



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SUMMARY
=======
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 of 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
normalIt is not:

second-countable
first-countable
metrizable
compact