International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 41-45

α-Scattered spaces

David A. Rose

Department of Mathematics, Southeastern College of the Assemblies of God, Lakeland 33801, Florida, USA

Received 26 March 1996; Revised 28 June 1996

Copyright © 1998 David A. Rose. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


α-scattered spaces, spaces whose α-topology is scattered, are introduced and used to slightly extend a recent result of A. V. Arhangel'skii and P. J. Collins [1]. Strong irresolvability of J. Foran and P. Liebnitz [6], is also characterized in terms ofthe α-topology, and it is shown that a recent theorem of Julian Dontchev [5] in essence maximally extends the Arhangel'skii-Collins result.