International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 3, Pages 519-530
doi:10.1155/S016117129300064X

Realcompactification and repleteness of Wallman spaces

Abstract

The extension of bounded lattice continuous functions on an arbitrary set X to the set of lattice regular zero-one measures on an algebra generated by a lattice (a Wallman-type space) is investigated.Next the subset of lattice regular zero-one measures on an algebra generated by a lattice which integrates all lattice continuous functions on X is introduced and various properties of it are presented.Finally conditions are established using repleteness criteria whereby the space of lattice regular zero-one measures on an algebra generated by a lattice which are countably additive (a Wallman-type space) is realcompact.