Related papers: Uniformly rigid spaces

We introduce the notion of echeloned spaces - an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly…

We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a…

In this paper we define a rigid rational homotopy type, associated to any variety $X$ over a perfect field $k$ of positive characteristic. We prove comparison theorems with previous definitions in the smooth and proper, and log-smooth and…

Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. In this article, we study uniformly finite homology of finitely generated amenable groups and…

We define the notion of affine rigidity of a hypergraph and prove a variety of fundamental results for this notion. First, we show that affine rigidity can be determined by the rank of a specific matrix which implies that affine rigidity is…

In this paper, we introduce the notion of partially ordered {\epsilon}-chainable metric spaces and we derive new coupled fixed point theorems for uniformly locally contractive mappings on such spaces.

The class of spaces such that their product with every Lindel\"of space is Lindel\"of is not well-understood. We prove a number of new results concerning such productively Lindel\"of spaces with some extra property, mainly assuming the…

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on…

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…

Here we propose a class of frameworks in the plane, braced polygons, that may be globally rigid and are analogous to convex polyopes in 3 space that are rigid by Cauchy's rigidity Theorem in 1813.

We introduce a matricial analogue of an Archimedean order unit space, which we call a $k$-AOU space. We develop the category of $k$-AOU spaces and $k$-positive maps and exhibit functors from this category to the category of operator systems…

This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…

We prove that the bundles with flat connections on configuration spaces associated to braided fusion categories, as well as the bundles with flat connections on moduli spaces of curves (conformal blocks) associated to modular fusion…

We suggest a concept of generalized `angles' in arbitrary real normed vector spaces. We give for each real number a definition of an `angle' by means of the shape of the unit ball. They all yield the well known Euclidean angle in the…

We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…

We say that a finite metric space $X$ can be embedded almost isometrically into a class of metric spaces $C$, if for every $\epsilon > 0$ there exists an embedding of $X$ into one of the elements of $C$ with the bi-Lipschitz distortion less…

Let $k$ be a discretely valued non-Archimedean field. We give an explicit description of analytic functions whose norm is bounded by a given real number $r$ on tubes of reduced $k$-analytic spaces associated to special formal schemes (those…

This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\bf L$. Theorems about expansions of complete…

For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that…

The notion of symmetry in polynomial rings with several indeterminates is generalized to polynomial rings over finite fields. Families of extensions of the projective line over a finite field of constants possessing this property are…