A Compactification with θ-Continuous Lifting Property

Abstract

1. Let X be a topological space, and let X′ be the set of all non-convergent ultrafilters on X. If A ⊆ X, let , and A* = A ∪ A′. If is a filter on X such that for all , then let. be the filter on X* generated by ; let be the filter on X* generated by . If exists then ; otherwise, .A convergence is defined on X* as follows: If x ∈ X, then a filter A → x in X* if and only if , where Vx(x) is the X neighborhood filter at x; , then in X* if and only if .