International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 605-609
doi:10.1155/S0161171291000819
On Lindelöf lattices and separation
Department of Mathematics, John Jay College of Criminal Justice, The City University of New York, 445 West 59th Street, New York 10019, NY, USA
Received 29 June 1990; Revised 17 October 1990
Copyright © 1991 George M. Eid. 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 a lattice of subsets of X. Some general properties of
Lindelöf, regular as well as normal lattices are investigated for their measure implications and their
relationship to separation properties. Moreover, we show that the generalized Wallman replete
space and the generalized Wallman prime complete space are Lindelöf spaces if and only if certain
measure relationships hold on ℒ.