On countable multiple point compactifications

Ordered Compactifications with Countable Remainders

Countable compactifications of topological spaces have been studied in [1], [5], [7], and [9]. In [7], Magill showed that a locally compact, T2 topological space X has a countable T2 compactification if and only if it has n-point T2 compactifications for every integer n ≥ 1. We generalize this theorem to T2-ordered compactifications of ordered topological spaces. Before starting our generalizat...

One-point Order-compactifications

We classify all one-point order-compactifications of a noncompact locally compact order-Hausdorff ordered topological space X. We give a necessary and sufficient condition for a one-point order-compactification of X to be a Priestley space. We show that although among the one-point order-compactifications of X there may not be a least one, there always is a largest one, which coincides with the...

The Point - Countable Base Problem

A bitopological point-free approach to compactifications

We study structures called d-frames which were developed by the last two authors for a bitopological treatment of Stone duality. These structures consist of a pair of frames thought of as the opens of two topologies, together with two relations which serve as abstractions of disjointness and covering of the space. With these relations, the topological separation axioms regularity and normality ...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...