International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 1, Pages 83-90
doi:10.1155/S0161171292000097
On normal lattices and separation and semi-separation of lattices
P.O. Box 1149, West Babylon, N.Y. 11704, USA
Received 26 October 1990; Revised 12 February 1991
Copyright © 1992 Robert W. Schutz. 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
This present paper is concerned with two main conditions, that of normality of a lattice, and separation and semi-separation of two lattices, both looked at using measure theoretic techniques. We look at each property using {0,1} two valued measures and associated {0,1} valued set functions.
For normal lattices we look at consequences of normality in terms of properties of their measures and closely allied set functions. For separation and semi-separation of two lattices, we investigate the realtionship between regular measures of both lattices, define the notion of weak going up and look at this notion in terms of separation and semi-separation. We then give necessary and sufficent conditions for semi-separation in terms of equality of two set fuctions, derived from regular measures on the smaller lattice on the larger lattice.