It is no exaggeration to say that the theory of separably injective spaces is quite different
from that of injective spaces. In this chapter we will explain why. Indeed, we will enter now in …

We give an overview of a research line concentrated on finding to which extent compactness
fails at the level of first uncountable cardinal and to which extent it could be recovered on …

We investigate the following problem posed by Cabello Sanchéz, Castillo, Kalton, and Yost:
Let K be a nonmetrizable compact space. Does there exist a nontrivial twisted sum of c 0 …

This paper studies the combinatorics of ideals which recently appeared in ergodicity results
for analytic equivalence relations. The ideals have the following topological representation …

The open graph dichotomy for a subset $ X $ of the Baire space ${}^\omega\omega $ states
that any open graph on $ X $ either admits a coloring in countably many colors or contains a …

We consider the class of Banach spaces Y for which c 0 admits a nontrivial twisted sum with
Y. We present a characterization of such spaces Y in terms of properties of the weak⁎ …

n-Luzin gaps - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals &
Books Search RegisterSign in View PDF Download full issue Search ScienceDirect Elsevier …

Basic orders were originally introduced in order to illuminate Tukey theory of directed sets
and in particular explain the phenomenon that Tukey reductions between definable directed …

An n-gap consists of n many pairwise orthogonal families of subsets of a countable set that
cannot be separated. We prove that for every positive integer n there is a finite basis for the …

Assume MA (κ). We show that for every real chain of size κ in the quotient Boolean algebra P
(ω)/fin we can find an almost chain of representatives such that every n∈ ω oscillates at …