arXiv subjects

O. Dovgoshey

Publications and source records attributed to O. Dovgoshey.

22 records · Page 2Linked to original sources

arXiv2011

Diameter and diametrical pairs of points in ultrametric spaces

Let F(X) be the set of finite nonempty subsets of a set X. We have found the necessary and sufficient conditions under which for a given function f:F(X)-->R there is an ultrametric on X such that f(A)=diam A for every A\in F(X). For finite nondegenerate ultrametric spaces (X,d) it is shown that X together with the subset of diametrical pairs of points of X forms a complete k-partite graph, k>= 2, and, conversely, every finite complete k-partite graph with k>=2 can be obtained by this way. We use this result to characterize the finite ultrametric spaces (X,d) having the minimal card{(x,y):d(x,y)=diam X, x,y \in X} for given card X.

math.MG↗

arXiv2011

Isometric embeddings of pretangent spaces in E^n

We prove some infinitesimal analogs of classical results of Menger, Schoenberg and Blumenthal giving the existence conditions for isometric embeddings of metric spaces in the finite-dimensional Euclidean spaces.

math.MG↗

arXiv2009

Tangent spaces to metric spaces and to their subspaces

We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces are completely determinated.

math.MG↗

arXiv2009

Ultrametricity and metric betweenness in tangent spaces to metric spaces

The paper deals with pretangent spaces to general metric spaces. An ltrametricity criterion for pretangent spaces is found and it is closely related to the metric betweenness in the pretangent spaces.

math.MG↗