相关论文: The Beckman-Quarles theorem for continuous mapping…

For positive integers $1 \leq k \leq n$ let $M_n$ be the algebra of all $n \times n$ complex matrices and $M_n^{\le k}$ its subset consisting of all matrices of rank at most $k$. We first show that whenever $k>\frac{n}{2}$, any continuous…

Let $A$, $B$ be algebras and $a\in A$, $b\in B$ a fixed pair of elements. We say that a map $\varphi:A\to B$ preserves products equal to $a$ and $b$ if for all $a_1,a_2\in A$ the equality $a_1a_2=a$ implies $\varphi(a_1)\varphi(a_2)=b$. In…

A function $f: \mathbb{Z} \to \mathbb{Q}^n$ is a $c$-quasihomomorphism if the Hamming distance between $f(x+y)$ and $f(x)+f(y)$ is at most $c$ for all $x,y \in \mathbb{Z}$. We show that any $c$-quasihomomorphism has distance at most some…

Suppose that $f_1,\ldots ,f_m : S(V)\to R$ are $m$ ($\geq 1$) continuous functions defined on the unit sphere in a Euclidean vector space $V$ of dimension $m+1$ satisfying $f_i(-v)=-f_i(v)$ for all $v\in S(V)$. The classical Borsuk-Ulam…

In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelism geometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the…

A well-known result from Brouwer states that any orientation preserving homeomorphism of the plane with no fixed points has an empty non-wandering set. In particular, an invariant compact set implies the existence of a fixed point. In this…

We prove that every nearly spherical, positively curved surface is the contractive, volume-preserving image of a round sphere. The proof combines three main tools: the Ricci flow on surfaces, the Kim-Milman construction, and a multiscale…

Let $I(X,K)$ be the incidence algebra of a finite connected poset $X$ over a field $K$ and $D(X,K)$ its subalgebra consisting of diagonal elements. We describe the bijective linear maps $\varphi:I(X,K)\to I(X,K)$ that strongly preserve the…

Let {\Lambda}\subsetR^{n}\timesR^{m} and k be a positive integer. Let f:R^{n}\rightarrowR^{m} be a locally bounded map such that for each ({\xi},{\eta})\in{\Lambda}, the derivatives D_{{\xi}}^{j}f(x):=|((d^{j})/(dt^{j}))f(x+t{\xi})|_{t=0},…

Distance-preserving mappings (DPMs) are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of the same or longer length such that every two distinct vectors are mapped to permutations with the same or…

We show that every nearly spherical manifold can be realized as the volume-preserving image of a round sphere, via the Brenier-McCann optimal transport map. This theorem extends Caffarelli's contraction theorem to nearly spherical manifolds…

The present paper generalizes the result from one of the papers by Galstyan. Namely, we consider two nonempty subsets $A$ and $B$ of a metric space $X$, and construct one-parametric family $F_r$ of subsets obtained by intersection between…

Brehm's extension theorem states that a non-expansive map on a finite subset of a Euclidean space can be extended to a piecewise-linear map on the entire space. In this note, it is verified that the proof of the theorem is constructive…

We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…

We establish a version of von Staudt's theorem on mappings which preserve harmonic quadruples for projective lines over (not necessarily commutative) rings with "sufficiently many" units, in particular 2 has to be a unit.

For a disk $D$ in the plane $\mathbb R^2$ and a plane map $f$, we give several conditions on the restriction of $f$ to the boundary $\partial D$ of $D$ which imply the existence of a fixed point of $f$ in some specified domain in $D$. These…

It is proved that any one-to-one edge map f from a 3-connected graph G onto a graph H, G and H possibly infinite, satisfying f(C) is a circuit in H whenever C is a circuit in G is induced by a vertex isomorphism. This generalizes a result…

The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to…

In this article, we prove two new versions of a theorem proven by Efron in [Efr65]. Efron's theorem says that if a function $\phi : \mathbb{R}^2 \rightarrow \mathbb{R}$ is non-decreasing in each argument then we have that the function $s…

Let $E_i$ be an oriented circle bundle over a closed oriented aspherical $n$-manifold $M_i$ with Euler class $e_i\in H^2(M_i;\mathbb{Z})$, $i=1,2$. We prove the following: (i) If every finite-index subgroup of $\pi_1(M_2)$ has trivial…