Realcompactification and repleteness of Wallman spaces (Q687860)

Summary: 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.