相关论文: Equivalent characterizations of non-Archimedean un…

A uniform space is said to be non-Archimedean if it is generated by equivalence relations. If $\lambda$ is a cardinal, then a non-Archimedean uniform space $(X,\mathcal{U})$ is $\lambda$-totally bounded if each equivalence relation in…

We explore a definition of uniformity on noncompact manifolds that does not require a Riemannian metric, but is equivalent to bounded gemetry. These are unfinished research notes (and will likely never be published), but since they were…

Given some non-Archimedean field $\mathbb{K}$ and some $\mathbb{K}$-linear space $X$, the usual way to define a norm over $X$ involves the {\em ultrametric inequality} $\|x+y\|\leq\max\{\|x\|,\|y\|\}$. In this note we will try to analyse…

We define a new category of non-archimedean analytic spaces over a complete discretely valued field, which we call uniformly rigid. It extends the category of rigid spaces, and it can be described in terms of bounded functions on products…

We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.

The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of…

We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity…

We generalize the theory of base norm spaces to the complex case, and further to the noncommutative setting relevant to `quantum convexity'. In particular, we establish the duality between complex Archimedean order unit spaces and complex…

In this paper, we approach the question if some of the separation axioms are equivalent in the class of asymmetric normed spaces. In particular, we make a remark on a known theorem which states that every $T_1$ asymmetric normed space with…

In this paper, we show that three different generalized similarities enclose all unitary and anti-unitary symmetries that induce exceptional points in lower-dimensional non-Hermitian systems. We prove that the generalized similarity…

For each $n$, we construct a separable metric space $\mathbb{U}_n$ that is universal in the coarse category of separable metric spaces with asymptotic dimension ($\mathop{asdim}$) at most $n$ and universal in the uniform category of…

Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…

In this paper,\ the authors define a space with an uniform base at non-isolated points, give some characterizations of images of metric spaces by boundary-compact maps, and study certain relationship among spaces with special base…

For the importance of differentiation theorems in metric spaces (starting with Pansu Rademacher type theorem in Carnot groups) and relations with rigidity of embeddings see the section 1.2 in Cheeger and Kleiner paper arXiv:math/0611954 and…

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…

In this article, we study the notions of $n$-isometries in non-Archimedean $n$-normed spaces over linear ordered non-Archimedean fields, and prove the Mazur-Ulam theorem in the spaces. Furthermore, we obtain some properties for…

The aim of this paper is to investigate the equivalence conditions for uniform perfectness of quasi-metric spaces. We also obtain the invariant property of uniform perfectness under quasim\"obius maps in quasi-metric spaces. In the end, two…

In this paper, we introduce the notions of pre-uniform spaces and pre-proximities and investigate some basic properties about them, where the definition of pre-uniformity here is different with the pre-uniformities which are studied in…

The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…

We provide an axiomatic approach to the theory of local tangent cones of regular sub-Riemannian manifolds and the differentiability of mappings between such spaces. This axiomatic approach relies on a notion of a dilation structure which is…