In this paper we present results about the structure of compact subsets of the first Baire
class. For example, we give a complete description of characters of points in such compacta …

The goal of this chapter is to reveal the power of descriptive set theory in penetrating the
structure of Banach spaces. The chapter is divided into three subchapters, each with its own …

In this article, we will focus on the interplay of weak topologies, smoothness and rotundity of
norms, biorthogonal systems and projectional resolutions of the identity operator in …

We review recent results concerning dynamical systems and their representations on
Banach spaces. As the enveloping (or Ellis) semigroup, which is associated to every …

We investigate non-separable Banach spaces whose norm-open sets are countable unions
of sets closed in the weak topology and a narrower class of Banach spaces with a network …

We discuss three problems of Koszmider on the structure of the spaces of continuous
functions on the Stone compact KA generated by an almost disjoint family A of infinite …

We consider the class of compact spaces $ K_A $ which are modifications of the well known
double arrow space. The space $ K_A $ is obtained from a closed subset $ K $ of the unit …

B< quad orl $, ˆ1 i 1 sa l ll $ aysf< quad$ a ˆ1 ne l $ ac t mu tipiat ve< quad c $ as $< quad
C< quad DM< quad$] 1 al $ nd< quad i< quad isc o$ n ˆ1 ect u rl $ e< noindent$ t 1 hl a ˆ1 tl …

The present work consists of three parts. In the first one we determine the prototypes of
separable Rosenthal compacta and we provide a classification theorem. The second part …

A compact space is said to be Rosenthal if it can be represented as a space of functions of
the first Baire class on some Polish space, equipped with the topology of pointwise …