WALLMAN COMPACTIFICATION AND SOBER SPACES

T(α, β)-spaces and the Wallman compactification

On Certain Wallman Spaces

Several generalized Wallman type spaces are considered as well as various lattices of subsets therein. In particular, regularity of these lattices and consequences are investigated. Also considered are necessary and sufficient conditions for these lattices to be Lindel6f as well as replete, prime complete, and fully replete.

Baire Spaces, Sober Spaces

In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers:

Sober Spaces and Continuations

A topological space is sober if it has exactly the points that are dictated by its open sets. We explain the analogy with the way in which computational values are determined by the observations that can be made of them. A new definition of sobriety is formulated in terms of lambda calculus and elementary category theory, with no reference to lattice structure, but, for topological spaces, this...

Induced Measures on Wallman Spaces

Let X be an abstract set and .t; a lattice of subsets ofX. To each lattice-regular measure we associate two induced measures and on suitable lattices of the Wallman space Is(L) and another measure IX’ on the space I,(L). We will investigate the reflection of smoothness properties of IX onto t, and Ix’ and try to set some new criterion for repleteness and measure repleteness.