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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 3, Pages 519-530
http://dx.doi.org/10.1155/S016117129300064X

Realcompactification and repleteness of Wallman spaces

Jersey City State College, 2039 Kennedy Boulevard, Jersey City, New Jersey 07305, USA

Received 20 August 1991; Revised 23 January 1992

Copyright © 1993 Hindawi Publishing Corporation. 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.