Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.
1 Some aspects in the Mathematical work of Jerzy Kakol.- 2 Weak barrelledness vs. P-spaces.- 3 On the topology of the sets of the real projections of the zeros of exponential polynomials.- 4 The density character of the space Cp(X).- 5 Compactness and distances to spaces of continuous functions and Fréchet spaces.- 6 Two classes of metrizable spaces lc-invariant.- 7 Characteristics of the Mackey topology for abelian topological groups.- 8 Bowen's Entropy for Endomorphisms of Totally Bounded Abelian.- 9 On preserved and unpreserved extreme points Groups.- 10 Cantor sets, Bernoulli shifts and linear dynamics.- 11 Some non-linear geometrical properties of Banach spaces.