International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 1, Pages 25-32
doi:10.1155/S0161171298000039
On lattice-topological properties of general Wallman spaces
Mathematics Department, Pace University Pace Plaza, New York 10038, NY, USA
Received 30 November 1995; Revised 25 March 1996
Copyright © 1998 Carmen Vlad. 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 arbitrary set and ℒ
a lattice of subsets of X such that ϕ,X∈ℒ.𝒜(ℒ) is the
algebra generated by ℒ and I(ℒ) consists of all zero-one valued finitely additive measures on
𝒜(ℒ). Various subsets of and I(ℒ) are considered and certain lattices are investigated as well as the topology of
closed sets generated by them. The lattices are investigated for normality, regularity, repleteness and
completeness. The topologies are similarly discussed for various properties such as
T2 and Lindelöf.