The new theory of ultrametric spaces
type: Item
instance of: scholarly article
title: The new theory of ultrametric spaces
zbMATH Open document ID: 0856.54033
DOI: 10.1007/BF01879736
published in: Periodica Mathematica Hungarica
publication date: 1997-02-24T00:00:00Z
review text: The author considers ultrametric spaces \((X,d,\Gamma)\) where \((\Gamma, \leq)\) is a partially ordered set. Ultrametric spaces such that any (nonempty) chain of balls has a nonempty intersection are called spherically complete. A (unique) fixed point theorem for spherically complete ultrametric spaces is proved. To show the interest in this theorem some modern examples of these spaces are given. Moreover, a spherically complete space \(X^*\) is associated to every ultrametric space \(X\) in such a way that if \((\Gamma,\leq)\) is a totally ordered set, then there is a canonical embedding from \(X\) into \(X^*\).
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 12J20
zbMATH DE Number: 926945
zbMATH Keywords: spherically complete ultrametric spaces
author: Paulo Ribenboim
reviewed by: Carlos Galindo
MaRDI profile type: Publication
cites work: Q3730636
cites work: The Banach fixed point theorem for ultrametric spaces
cites work: Fixed points, combs and generalized power series
cites work: Ordering the set of antichains of an ordered set
description: scientific article; zbMATH DE number 926945