About remainders in compactifications of paratopological groups

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...

A remark on Remainders of homogeneous spaces in some compactifications

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

On Compactifications with Path Connected Remainders

We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon. Connectedness and compactness are two fundamental topological properties. A natural question is whether a given space admits a connected (Hausdorff) compactification. This question has been st...

Menger remainders of topological groups

In this paper we discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance, we show that such a remainder is Hurewicz if and only it is σ-compact. Also, the existence of a Scheepers non-σ-compact remainder of a topological group follows from CH and yields a P -point, and hence is independent of Z...

Samuel Compactifications of Automorphism Groups

Cayley Compactifications of Abelian Groups

Following work of Rieffel [1], in this document we define the Cayley compactification of a discrete group G together with a set of generators S. We use algebraic methods in the general case to construct an explicit presentation of Cayley compactifications. In the particular case of Z, we use geometric methods to demonstrate a strong connection between the Cayley compactification and the polytop...