Related papers: Coproducts of proximity spaces

In 2014, Gromov conjectured that sequences of manifolds with nonnegative scalar curvature should have subsequences which converge in some geometric sense to limit spaces with some notion of generalized nonnegative scalar curvature. In…

We first prove that for all compact metrizable spaces, there exists a topological embedding of the compact metrizable space into each of the sets of compact metric spaces which are connected, path-connected, geodesic, or CAT(0), in the…

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to M\"obius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with…

Let $T$ be a topological space admitting a compatible proper metric, that is, a locally compact, separable and metrisable space. Let $\mathcal{M}^T$ be the non-empty set of all proper metrics $d$ on $T$ compatible with its topology, and…

We study geodesically complete and locally compact Hadamard spaces X whose Tits boundary is a connected irreducible spherical building. We show that X is symmetric iff complete geodesics in X do not branch and a Euclidean building…

In a previous paper the authors developed a H^1-BMO theory for unbounded metric measure spaces $(M,\rho,m)$ of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and…

In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, $\omega$-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff…

Given a Hermitian symmetric space $M$ of noncompact type, we give a complete description of the horofunctions in the metric compactification of $M$ with respect to the Carath\'eodory distance, via the realisation of $M$ as the open unit…

In this paper we show that the proximity inductive dimension defined by Isbell agrees with the Brouwer dimension originally described by Brouwer on the class of compact Hausdorff spaces. Consequently, Fedorchuk's example of a compact…

We study completeness properties of Sobolev metrics on the space of immersed curves and on the shape space of unparametrized curves. We show that Sobolev metrics of order $n\geq 2$ are metrically complete on the space $\mathcal…

We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with…

A metric space $X$ is quasisymmetrically co-Hopfian if every quasisymmetric embedding of $X$ into itself is onto. We construct the first examples of metric spaces homeomorphic to the universal Menger curve and higher dimensional…

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces $X=G/K$ of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable $G$-invariant Finsler metric on $X$. As…

We introduce and study skew product Smale endomorphisms over finitely irreducible topological Markov shifts with countable alphabets. We prove that almost all conditional measures of equilibrium states of summable and locally Holder…

We associate, with every infinite word over a finite alphabet, an increasing sequence of rooted finite graphs, which provide a discrete approximation of the famous Sierpi\'nski carpet fractal. Each of these sequences converges, in the…

We highlight a condition, the approaching geodesics property, on a proper geodesic Gromov hyperbolic metric space, which implies that the horofunction compactification is topologically equivalent to the Gromov compactification. It is known…

We study comparison estimates on metric measure spaces admitting a synthetic variable Ricci curvature lower bound. We obtain geometric and functional inequalities assuming that the deficit of the lower bound from a given constant is…

A locally conformally product (LCP) structure on compact manifold $M$ is a conformal structure $c$ together with a closed, non-exact and non-flat Weyl connection $D$ with reducible holonomy. Equivalently, an LCP structure on $M$ is defined…

We investigate for which compactifications $\gamma\omega$ of the discrete space of natural numbers $\omega$, the natural copy of the Banach space $c_0$ is complemented in $C(\gamma\omega)$. We show, in particular, that the separability of…

We give an elementary proof of a compact embedding theorem in abstract Sobolev spaces. The result is first presented in a general context and later specialized to the case of degenerate Sobolev spaces defined with respect to nonnegative…