相关论文: Linear algebra and unification of geometries in al…

We give a detailed description of the possible limits in the equivariant-Gromov-Hausdorff sense of sequences $(X_j,G_j)$, where the $X_j$'s are proper, geodesically complete, uniformly packed, CAT$(0)$-spaces and the $G_j$'s are closed,…

Various theorems on convergence of general space homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring $Q$--homeomorphisms are obtained. In particular, it was established by…

In this paper, we characterise metric spaces which have topologically connected Higson coronas. The characterisation is given by a natural categorical condition applied in the coarse category. We also give a characterisation in terms of…

Sofic groups generalise both residually finite and amenable groups, and the concept is central to many important results and conjectures in measured group theory. We introduce a topological notion of a sofic boundary attached to a given…

We prove sandwich theorems and a Tauberian theorem in the space of compact metric measure spaces, endowed with the Gromov-Hausdorff-Prokhorov (GHP) topology. These results hold with respect to a close relative of Gromov's Lipschitz order.…

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own case - similarity shapes - the shape spaces are…

We prove the equivalence between geometric and analytic definitions of quasiconformality for a homeomorphism $f\colon X\rightarrow Y$ between arbitrary locally finite separable metric measure spaces, assuming no metric hypotheses on either…

Given a metrizable topological vector space, we can also use its von Neumann bornology or its bornology of precompact subsets to do analysis. We show that the bornological and topological approaches are equivalent for many problems. For…

A topological space is said to be cardinality homogeneous if every nonempty open subset has the same cardinality as the space itself. Let $X$ and $Y$ be cardinality homogeneous metric spaces of the same cardinality. If there exists a…

We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to David and Semmes in the case of sufficiently large co-dimension,…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

A generalized topology in a set $X$ is a collection $\text{Cov}_X$ of families of subsets of $X$ such that the triple $(X,\bigcup \text{Cov}_X,\text{Cov}_X)$ is a generalized topological space in the sense of Delfs and Knebusch. In this…

In this paper, pointwise convergence, uniform convergence and compact convergence of sequences of holomorphic functions on an open subset of the complex plane are compared from a linear point of view. In fact, it is proved the existence of…

We show that the topological full group of a Hausdorff ample groupoid with compact unit space coincides with the group of homotopy classes of invertible isometries in pseudofunction algebras associated with the groupoid. Moreover, if the…

We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of…

The $K$-theory of the stable Higson corona of a coarse space carries a canonical ring structure. This ring is the domain of an unreduced version of the coarse co-assembly map of Emerson and Meyer. We show that the target also carries a ring…

The main goal of this paper is to investigate the structure of Hopf algebras with the property that either its Jacobson radical is a Hopf ideal or its coradical is a subalgebra. In order to do that we define the Hochschild cohomology of an…

For a metric space $(X,d)$, Beer, Naimpally, and Rodriguez-Lopez in ([17]) proposed a unified approach to explore set convergences via uniform convergence of distance functionals on members of an arbitrary family $\mathcal{S}$ of subsets of…

We compactify the classical moduli variety of compact Riemann surfaces by attaching moduli of (metrized) graphs as boundary. The compactifications do not admit the structure of varieties and patch together to form a big connected moduli…