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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 3, Pages 553-559
http://dx.doi.org/10.1155/S0161171297000744

Normal lattices and coseparation of lattices

Department of Mathematics, Sacred Heart University, 5151 Park Avenue, Fairfield 06432-1000, CT, USA

Received 19 September 1995

Copyright © 1997 Hindawi Publishing Corporation. 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 non-empty set, and let be a lattice of subsets of X such that , X. We first summarize a number of known conditions which are equivalent to being normal. We then develop new equivalent conditions in terms of set functions associated with μI(), the set of all non-trivial, zero-one valued finitely additive measures on the algebra generated-by . We finally generalize all the above to the situation where 1 and 2 are a pair of lattices of subsets of X with 12, and where we obtain equivalent conditions for 1 to coseparate 2.