相关论文: A proof of uniqueness of the Gurarii space

In this short note, we answer two questions about Gurariy spaces asked in the literature in the affirmative. We also prove the analogue of one of the results for the noncommutative Guariy space.

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the…

We give a new short proof for the uniqueness of the universal minimal space. The proof holds for the uniqueness of the universal object in every collection of topological dynamical systems closed under taking projective limits and…

We show that the isometry group of the bounded Urysohn space is simple. This extends previous work by the authors.

We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.

Some examples and basic properties of ultrametric spaces are briefly discussed.

In this note, we will give a short proof of an identity for cubic partitions.

Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.

We show that the classes of partial isometries in finite-dimensional polyhedral spaces and in finite-dimensional rational polyhedral spaces do not have the weak amalgamation property. This implies that the linear isometry group of the…

We realize the noncommutative Gurarij space $\mathbb{NG}$ defined by Oikhberg as the Fra\"{\i}ss\'{e} limit of the class of finite-dimensional $1$-exact operator spaces. As a consequence we deduce that the concommutative Gurarij space is…

We prove a comparison isomorphism between singular cohomology and sheaf cohomology.

Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.

In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.

A proof of the isometric embedding of a given two-metric in E^3 of class C^1. The method uses the theory of first order partial differential equations. The curvature of the metric plays no role in the proof.

The purpose of the paper is to present an short proof of the Chuang's inequality.

The Gurari\u{\i} space is the unique separable Banach space $\mathbb{G}$ which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every $\varepsilon>0$, for all finite-dimensional normed spaces $E…

We introduce a Zariskian analogue of the theory of Huber's adic spaces.

We study the space of Riemannian metrics over a compact manifold equipped with the Ebin metric. We characterize its self-isometries and prove that two such spaces are isometric if and only if their underlying manifolds are diffeomorphic.

The issue and proof of Gurzadyan theorem are presented concisely, avoiding tedious and unnecessary calculations that would mask what is essential. The goal is to provide a good mathematical and physical understanding of the theorem, making…