The immersion of ultrametric spaces into Hahn spaces
type: Item
instance of: scholarly article
title: The immersion of ultrametric spaces into Hahn spaces
zbMATH Open document ID: 1190.54017
author: Paulo Ribenboim
published in: Journal of Algebra
publication date: 2010-04-21T00:00:00Z
review text: The immersion of an ultrametric space with totally ordered set of distances into a spherically complete ultrametric space was established independently by \textit{S. Priess-Crampe} and \textit{P. Ribenboim} [Abh. Math. Semin. Univ. Hamb. 67, 19--31 (1997; Zbl 0887.54029)] and by \textit{E. Schörner} [Result. Math. 29, No.~3--4, 361--370 (1996; Zbl 0866.54028)]. In the present paper the author proves the theorem for ultrametric spaces having a set of distances which is not assumed to be totally ordered. Virtual points and the skeleton of an ultrametric space play an important role in these investigations. He also establishes a similar theorem for ultrametric torsion-free abelian additive groups.
reviewed by: Hans Peter Künzi
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 5696918
zbMATH Keywords: ultrametric spaces
zbMATH Keywords: Hahn spaces
zbMATH Keywords: virtual points
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.11.032
OpenAlex ID: W2030194314
cites work: Totalgeordnete Moduln
cites work: Embedding Theorems for Abelian Groups with Valuations
cites work: Generalized ultrametric spaces. I
cites work: Generalized ultrametric spaces. II
cites work: Homogeneous ultrametric spaces
cites work: On immediate extensions of ultrametric spaces
DOI: 10.1016/J.JALGEBRA.2009.11.032
description: scientific article; zbMATH DE number 5696918