Remainders of H-closed extensions

Pseudo Algebraically Closed Extensions

Nonhomogeneity of Remainders, Ii

We present an example of a separable metrizable topological group G having the property that no remainder of it is (topologically) homogeneous. 1. Introduction. All topological spaces under discussion are Tychonoff. A space X is homogeneous if for any two points x, y ∈ X there is a homeomorphism h from X onto itself such that h(x) = y. If bX is a com-pactification of a space X, then bX \ X is c...

On Pseudo Algebraically Closed Extensions of Fields

The notion of ‘Pseudo Algebraically Closed (PAC) extensions’ is a generalization of the classical notion of PAC fields. In this work we develop a basic machinery to study PAC extensions. This machinery is based on a generalization of embedding problems to field extensions. The main goal is to prove that the Galois closure of any proper separable algebraic PAC extension is its separable closure....

Existentially Closed R-domains in Regular Extensions

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...