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
Jersey City State College, 2039 Kennedy Boulevard, Jersey City 07305, New Jersey, USA
Received 20 August 1991; Revised 23 January 1992
Copyright © 1993 James Camacho. 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
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.