International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 553-559
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 Barry B. Mittag. 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 be an arbitrary non-empty set, and let be a lattice of subsets of such that ,
. 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 , 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 and are a pair of lattices of subsets of with
, and where we obtain equivalent conditions for to coseparate .