Topological properties of generalized Wallman spaces and lattice relations

Abstract

Let X be an abstract set and ℒ be a lattice of subsets of X. Associated with the pair (X,ℒ) are a variety of Wallman-type topological spaces. Some of these spaces generalize very important topological spaces such as the Stone-Čech compactification, the real compactification, etc. We consider the general setting and investigate how the properties of ℒ reflect over to the general Wallman Spaces and conversely. Completeness properties of the lattices in the Wallman Spaces are investigated, as well as the interplay of topological properties of these spaces such as T2, regularity and Lindelöf with ℒ.

Keywords

• Generalized Wallman Spaces and their topological properties
• lattice repleteness and completeness
• zero-one valued measures
• smoothness properties of measures.