Some Special Classes of Topological Groups

Abstract

Chapter 4 is one of the main in the book. It develops, in various directions, the central theme that we have already touched upon in previous chapters — how the presence of a synchronized algebraic structure in uences properties of a topology. We consider below, from this point of view, a series of most important topological properties such as compactness (Sections 4.1 and 4.2), Čech-completeness and featheriness (Section 4.3), the P-property, extremal disconnectedness (Sections 4.4 and 4.5), the Fréechet{Urysohn property and weak first countability (Section 4.7). The choice of the above mentioned properties is justified not only by their remarkable role in General Topology, but by the fact that each of them has already been a subject of deep and unexpected results in topological algebra.