Let K be a locally compact space, and denote by C0 (K) the Banach space of all continuous
functions on K that vanish at infinity, taken with the uniform norm. This fundamentally …

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 …

In 1973, Diestel published his seminal paper Grothendieck spaces and vector measures that
drew a connection between Grothendieck spaces (Banach spaces for which weak-and …

We present new methods to obtain singular twisted sums $ X\oplus _\Omega X $(ie, exact
sequences $0\to X\to X\oplus _\Omega X\to X\to 0$ in which the quotient map is strictly …

We investigate Galvin's property, a striking feature of the filter of closed unbounded subsets
of an infinite cardinal. In particular, we continue the work of Abraham and Shelah (J …

In this paper we present a method to obtain Banach spaces of universal and almost-
universal disposition with respect to a given class M of normed spaces. The method …

We show that for each p∈(0, 1] there exists a separable p-Banach space G p of almost
universal disposition, that is, having the following extension property: for each ε> 0 and each …

Banach spaces that are complemented in the second dual are characterised precisely as
those spaces X which enjoy the property that for every amenable semigroup S there exists …

arXiv:1001.4888v2 [math.LO] 11 Apr 2011 Page 1 arXiv:1001.4888v2 [math.LO] 11 Apr 2011
MULTIPLE GAPS ANTONIO AVILÉS AND STEVO TODORCEVIC Abstract. We study a …

We present a purely category-theoretic characterization of retracts of Fraïssé limits. For this
aim, we consider a natural version of injectivity with respect to a pair of categories (a …