Related papers: Sailing over three problems of Koszmider

Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum…

For any cardinal number $\kappa$ and an index set $\Gamma$, $\Sigma_\kappa$-product of real lines consists of elements of ${\mathbb R}^\Gamma$ having $<\kappa$ nonzero coordinates. A compact space $K$ is $\kappa$-Corson compact if it can be…

For every well founded tree $\mathcal{T}$ having a unique root such that every non-maximal node of it has countable infinitely many immediate successors, we construct a $\mathcal{L}_\infty$-space $X_{\mathcal{T}}$. We prove that for each…

Let $\Gamma$ be a finitely generated cocompact lattice of a totally disconnected locally compact group $G$, and $C$ a dense subgroup of $G$ that contains and commensurates $\Gamma$. We study the problem of describing all finitely generated…

Symmetry plays a basic role in variational problems (settled e.g. in $\mathbb R^{n}$ or in a more general manifold), for example to deal with the lack of compactness which naturally appear when the problem is invariant under the action of a…

We prove that if $K$ and $L$ are compact spaces and $C(K)$ and $C(L)$ are isomorphic as Banach spaces then $K$ has a $\pi$-base consisting of open sets $U$ such that $\bar{U}$ is a continuous image of some compact subspace of $L$. This…

Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space E with Riemannian metric g. Given an (augmented) Fredholm filtration F of M by finite-dimensional submanifolds (M_n), we associate to the triple…

In his PhD Thesis Konstantinos Beros proved a number of results about compactly generated subgroups of Polish groups. Such a group is K-sigma - the countable union of compact sets. He notes that the group of rationals under addition with…

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable…

For every space $X$ let $\mathcal K(X)$ be the set of all compact subsets of $X$. Christensen \cite{c:74} proved that if $X, Y$ are separable metrizable spaces and $F\colon\mathcal{K}(X)\to\mathcal{K}(Y)$ is a monotone map such that any…

We show that, if a simple $C^{*}$-algebra $A$ is topologically finite-dimensional in a suitable sense, then not only $K_{0}(A)$ has certain good properties, but $A$ is even accessible to Elliott's classification program. More precisely, we…

Extending a result of the first author and Katsura, we prove that for every UHF algebra $A$ of infinite type, in every uncountable cardinality $\kappa$ there are $2^\kappa$ nonisomorphic approximately matricial C*-algebras with the same…

In the present article we introduce and study a class of topological reflection spaces that we call Kac-Moody symmetric spaces. These generalize Riemannian symmetric spaces of non-compact type. We observe that in a non-spherical Kac-Moody…

Improving a result of M. Talagrand, under the assumption of a weak form of Martin's axiom, we construct a totally disconnected compact Hausdorff space $K$ such that the Banach space $C(K)$ of continuous real-valued functions on $K$ is a…

Let $A$ be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if $f,f_1,\dots,f_n\in A$ satisfy $|f|\leq \sum_{j=1}^n |f_j|$, does there exist $g_j\in A$ and a constant…

We provide an abstract categorical framework that relates the Cuntz semigroups of the C$^*$-algebras $A$ and $A\otimes \mathcal{K}$. This is done through a certain completion of ordered monoids by adding suprema of countable ascending…

It is known that $C(X)$ is algebraically closed if $X$ is a locally connected, hereditarily unicoherent compact Hausdorff space. For such spaces, we prove that if $F:C(X) \to C(X)$ is given by an everywhere convergent power series with…

For a compactification $\alpha X$ of a Tychonoff space $X$, the algebra of all functions $f\in C(X)$ that are continuously extendable over $% \alpha X$ is denoted by $C_{\alpha}(X)$. It is shown that, in a model of $\textbf{ZF}$, it may…

In the paper, we recall the Wallman compactification of a Tychonoff space $T$ (denoted by $\text{Wall}(T)$) and the contribution made by Gillman and Jerison. Motivated by the Gelfand-Naimark theorem, we investigate the homeomorphism between…

For a compact Hausdorff space $K$, we give descriptions of the dual of $C(K)^\delta$, the Dedekind completion of the Banach lattice $C(K)$ of continuous, real-valued functions on $K$. We characterize those functionals which are…