Realcompactification and repleteness of Wallman spaces

James Camacho

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-12

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.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:215328

DOI: 10.1155/S016117129300064X

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