International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 920737, 9 pages
Research Article

Topological Aspects of the Product of Lattices

Department of Mathematics, Pace University, Pleasantville, NY 10570, USA

Received 8 June 2011; Accepted 23 July 2011

Academic Editor: Alexander Rosa

Copyright © 2011 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.


Let 𝐗 be an arbitrary nonempty set and 𝐋 a lattice of subsets of 𝐗 such that , X L . 𝐀 ( 𝐋 ) denotes the algebra generated by 𝐋 , and 𝐌 ( 𝐋 ) denotes those nonnegative, finite, finitely additive measures on 𝐀 ( 𝐋 ). In addition, 𝐈 ( 𝐋 ) denotes the subset of 𝐌 ( 𝐋 ) which consists of the nontrivial zero-one valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces, and products of a variety of measures.