International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 717-722

Topological properties of generalized Wallman spaces and lattice relations

James A. Allan

Long Island University, Department of Mathematics, Brooklyn 11201, New York, USA

Received 6 October 1994; Revised 29 March 1995

Copyright © 1996 James A. Allan. 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.


Let X be an abstract set and be a lattice of subsets of X. Associated with the pair (X,) are a variety of Wallman-type topological spaces. Some of these spaces generalize very important topological spaces such as the Stone-Čech compactification, the real compactification, etc. We consider the general setting and investigate how the properties of reflect over to the general Wallman Spaces and conversely. Completeness properties of the lattices in the Wallman Spaces are investigated, as well as the interplay of topological properties of these spaces such as T2, regularity and Lindelöf with .