Approximation relations on the posets of pseudometrics and of pseudoultrametrics

Abstract

We show that non-trivial "way below" and "way above" relations on the posets of all pseudometrics and of all pseudoultrametrics on a fixed set X are possible if and only if the set X is finite.

Authors and Affiliations

S. I. Nykorovych

Keywords

Related Articles

(p,q) th order oriented growth measurement of composite p -adic entire functions

Let us consider K be a complete ultrametric algebraically closed field and suppose A(K) be the K-algebra of entire functions on K. For any p-adic entire functions f∈A(K) and r>0, we denote by |f|(r) the number sup{|f(x)|...

Geometry of hypersurfaces of a quarter symmetric non metric connection in a quasi-Sasakian manifold

The purpose of the paper is to study the notion of CR-submanifold and the existence of some structures on a hypersurface of a quarter symmetric non metric connection in a quasi-Sasakian manifold. We study the existence o...

Divisor problem in special sets of Gaussian integers

Let $A_1$ and $A_2$ be fixed sets of gaussian integers. We denote by $\tau_{A_1, A_2}(\omega)$ the number of representations of $\omega$ in form $\omega=\alpha\beta$, where $\alpha \in A_1, \beta \in A_2$. We construct t...

The nonlocal problem for the 2n differential equations with unbounded operator coefficients and the involution

We study a problem with periodic boundary conditions for a 2n-order differential equation whose coefficients are non-self-adjoint operators. It is established that the operator of the problem has two invariant subspaces...

Superextensions of three-element semigroups

A family $\mathcal{A}$ of non-empty subsets of a set $X$ is called an {\em upfamily} if for each set $A\in\mathcal{A}$ any set $B\supset A$ belongs to $\mathcal{A}$. An upfamily $\mathcal L$ of subsets of $X$ is said to...

Download PDF file
  • EP ID EP262985
  • DOI 10.15330/cmp.8.1.150-157
  • Views 87
  • Downloads 0

How To Cite

S. I. Nykorovych (2016). Approximation relations on the posets of pseudometrics and of pseudoultrametrics. Карпатські математичні публікації, 8(1), 150-157. https://europub.co.uk/articles/-A-262985