International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 9, Pages 597-603
On -cluster sets and -closed spaces
Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Calcutta 700 019, India
Received 15 July 1996; Revised 3 November 1997
Copyright © 2000 M. N. Mukherjee and Atasi Debray. 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.
A new type of cluster sets, called -cluster sets, of functions
and multifunctions between topological spaces is introduced,
thereby providing a new technique for studying -closed spaces.
The deliberation includes an explicit expression of -cluster set
of a function. As an application, characterizations of Hausdorff
and -closed topological spaces are achieved via such cluster