International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 49-59

On Alexandrov lattices

Albert Gorelishvili

Department of Mathematics, New York Institute of Technology, Old Westbury 11568, New York, USA

Received 10 October 1991; Revised 20 January 1992

Copyright © 1993 Albert Gorelishvili. 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.


By an Alexandrov lattice we mean a δ normal lattice of subsets of an abstract set X, such that the set of -regular countably additive bounded measures is sequentially closed in the set of -regular finitely additive bounded measures on the algebra generated by with the weak topology.

For a pair of lattices 12 in X sufficient conditions are indicated to determine when 1 Alexandrov implies that 2 is also Alexandrov and vice versa. The extension of this situation is given where T:XY and 1 and 2 are lattices of subsets of X and Y respectively and T is 12 continuous.