Related papers: Barr-coexactness for metric compact Hausdorff spac…

We introduce a hypertopology, induced by an inframetric up to full quantum isometry, on the class of pointed proper quantum metric spaces, which are separable, possibly non-unital, C*-algebras endowed with an analogue of the Lipschitz…

In this work, a metric is presented on the set of boundedly-compact pointed metric spaces that generates the Gromov-Hausdorff topology. A similar metric is defined for measured metric spaces that generates the Gromov-Hausdorff-Prokhorov…

We extend Yosida's 1941 version of Stone-Gelfand duality to metrically complete unital lattice-ordered groups that are no longer required to be real vector spaces. This calls for a generalised notion of compact Hausdorff space whose points…

We show in detail that every compact countable subset of a metric space is homeomorphic to a countable ordinal number, which extends a result given by Mazurkiewicz and Sierpinski for finite-dimensional Euclidean spaces. In order to achieve…

We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the…

Let Y be an absolute neighborhood retract (ANR) for the class of metric spaces and let X be a Hausdorff space. Let map(X,Y) denote the space of continuous maps from X to Y with the compact open topology. It is shown that if X is a CW…

One shows for Banach bundles in a certain class that having a second countable locally compact Hausdorff base space and separable fibers implies the separability of the Banach space of the all sections that vanish at infinity. In the…

In this paper the notion of modular cone metric space is introduced and some properties of such spaces are investigated. Also we define convex modular cone metric which takes values in CR(Y) where Y is a compact Hausdorff space. Then a…

We answer a question of Piotr Minc by proving that there is no compact metrizable space whose set of components contains a unique topological copy of every metrizable compactification of a ray (i.e. a half-open interval) with an arc (i.e.…

We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than $k$ can be always mapped onto a $k$-dimensional cube by a Lipschitz map. We also show that…

The "weakly Hausdorff" property for pseudoradial spaces fails to be naturally characterized by unique convergence of transfinite sequences. In response, we develop the category $\mathbf{SPsRad}$ of strongly pseudoradial spaces, compactly…

We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic…

We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…

Stone duality is an indispensable tool for the study of compact, zero-dimensional, Hausdorff spaces. In the case of general compact Hausdorff spaces one can get quite a bit of mileage by considering the `Wallman duality' between compact…

We introduce and study the framework of compact metric structures and their associated notions of isomorphisms such as homeomorphic and bi-Lipschitz isomorphism. This is subsequently applied to model various classification problems in…

The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…

The category of compact Hausdorff locales is a pretopos which is filtral, meaning that every object is covered by one whose subobject lattice is isomorphic to the lattice of filters of complemented elements. We show that any filtral…

This paper is about geometric and topological properties of a proper CAT(0) space $X$ which is cocompact - i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in $X$ can…

We construct a topology on the class of pointed proper quantum metric spaces which generalizes the topology of the Gromov-Hausdorff distance on proper metric spaces, and the topology of the dual propinquity on Leibniz quantum compact metric…

The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type theorem for Hausdorff dimension: For any $0<\beta<\alpha$, any compact metric space $X$ of Hausdorff dimension $\alpha$…