International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 735-740

On spaces whose nowhere dense subsets are scattered

Julian Dontchev1 and David Rose2

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.


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.