International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 717-722
doi:10.1155/S0161171296000981
Topological properties of generalized Wallman spaces and lattice relations
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.
Abstract
Let X be an abstract set and ℒ be a lattice of subsets of X. Associated with the
pair (X,ℒ) 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 ℒ 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 ℒ.