International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 735-740
doi:10.1155/S0161171298001021
On spaces whose nowhere dense subsets are scattered
1Department of Mathematics, University of Helsinki, Hallituskatu 15, Helsinki 10 00014, Finland
2Department of Mathematics, Southeastern College, 1000 Longfellow Boulevard, Lakeland 33801-6099, Florida, USA
Received 12 November 1996
Copyright © 1998 Julian Dontchev and David 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.
Abstract
The aim of this paper is to study the class of N-scattered spaces, i.e. the spaces
whose nowhere dense subsets are scattered. The concept was recently used in a decomposition of
scatteredness — a topological space
(X,τ)
is scattered if and only if X is α-scattered (= its α-topology
is scattered) and N-scattered.