Related papers: External characterization of I-favorable spaces

This note provides some technical support to the proof of a result of W. Winter which shows that two unital separable simple amenable ${\cal Z}$-absorbing C*-algebras with locally finite decomposition property satisfying the UCT whose…

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg…

In this paper, we present a characterization of compact quantum metric spaces in terms of finite dimensional approximations. This characterization naturally leads to the introduction of a matrix analogue of a compact quantum metric space.…

Motivated by Exel's inverse semigroup approach to combinatorial C*-algebras, in a previous work the authors defined an inverse semigroup associated with a labelled space. We construct a representation of the C*-algebra of a labelled space,…

We introduce and study a natural notion of selflessness for inclusions of C*-probability spaces, which in particular implies that all intermediate C*-algebras are selfless in the sense of Robert. We identify natural sources of selfless…

A reduction of properties (invariants) of compact sets of real numbers to properties of countable orders is presented here. Discussed here is also an embedding property of some compact sets that are called t$\mathbb R$-sets. Among others,…

Below, by space we mean a separable metrizable zero-dimensional space. It is studied when the space can be embedded in a Cantor set while maintaining the algebraic structure. Main results of the work: every space is an open retract of a…

We study some model-theoretic notions in NIP by means of spectral topology. In the o-minimal setting we relate the o-minimal spectrum with other topological spaces such as the real spectrum and the space of infinitesimal types of Peterzil…

We show that nuclear C*-algebras have a refined version of the completely positive approximation property, in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps. We use…

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.

A characterisation of trivial 1-cohomology for a broad class of metric spaces is presented. The condition ties cohomology and connectedness properties of open sets.

In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over commutative fields. In the…

We introduce the notion of strong embeddability for a metric space. This property lies between coarse embeddability and property A. A relative version of strong embeddability is developed in terms of a family of set maps on the metric…

In this paper we consider the problem of characterization of topological spaces that embed into countably compact Hausdorff spaces. We study the separation axioms of subspaces of countably compact Hausdorff spaces and construct an example…

It is shown that finitely presented icc inner amenable groups yield strongly 1-bounded II_1 factors.

For a convergent series with positive terms, we prove that the $\ell^\infty$ product space of bounded subspaces of the Gromov-Hausdorff space can be isometrically embedded into the Gromov-Hausdorff space, where each subspace consists of…

We use topological consequences of PFA, MA$_{\omega_1}$(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additionals properties are compact in these models.

In applications it is useful to know whether a topological preordered space is normally preordered. It is proved that every $k_\omega$-space equipped with a closed preorder is a normally preordered space. Furthermore, it is proved that…

We introduce two notions of amenability for a Banach algebra $\cal A$. Let $I$ be a closed two-sided ideal in $\cal A$, we say $\cal A$ is $I$-weakly amenable if the first cohomology group of $\cal A$ with coefficients in the dual space…

We study the space of complete Riemannian metrics of nonnegative curvature on the plane equipped with the C^k topology. If k is infinite, we show that the space is homeomorphic to the separable Hilbert space. For any k we prove that the…