Let A be a Tychonoff space. As is well known, the points of the Stone-Cech compactification ßX "are" the zero-set ultrafilters of X, and the points of the Hewitt real-compactification vX are the zero-set ultrafilters which are closed under countable intersection. It is shown here that a zeroset ultrafilter is a point of the Dieudonné topological completion SX iff the family of complementary coz...

In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.

This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or σ-complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.

We study maximal independent families (hereafter: mifs) and their applications to topological questions. We prove that if there exists either an (ω, ω1)-mif of size 2 ω1 with open density ω, or an (ω, ω1)-mif of size ≤ 2, then there exists an ω-resolvable, not maximally resolvable, Tychonoff space.