The sequential defect of the cross topology is \(\omega _ 1\)
With the aid of inductive limits, \textit{A. V. Arkhangel'skij} and \textit{S. P. Franklin} [Mich. Math. J. 15, 313-320 (1968; Zbl 0167.511)] constructed a countable, sequential, homogeneous Hausdorff space in which the topological closure is obtained by precisely \(\omega_ 1\) iterations of the sequential closure. This paper shows that the rational plane \(Q^ 2\) with the cross topology has the properties stated above. Here the cross topology is the topology in which a set A is open if and only if every ''horizontal'' or ''vertical'' sequence, converging in the usual way to a point in A, is eventually in A.
scientific article; zbMATH DE number 3909311