International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 22, Pages 1169-1177
doi:10.1155/S0161171204105012
Minimal sequential Hausdorff spaces
Department of Mathematics, Morgan State University, Baltimore 21251, MD, USA
Received 15 May 2001
Copyright © 2004 Bhamini M. P. Nayar. 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
A sequential space (X,T) is called minimal sequential if no sequential topology on X is strictly weaker than T. This paper begins the study of minimal sequential Hausdorff spaces. Characterizations of minimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of spaces, for example, minimal Hausdorff spaces, countably compact spaces, H-closed spaces, SQ-closed spaces, and subspaces of minimal sequential spaces, are investigated. While the property of being sequential is not (in general) preserved by products, some information is provided on the question of when the product of minimal sequential spaces is minimal sequential.