Separated totally convex spaces
type: Item
instance of: scholarly article
title: Separated totally convex spaces
zbMATH Open document ID: 0594.46064
DOI: 10.1007/BF01168830
author: Dieter Pumplün
author: Helmut Röhrl
published in: Manuscripta Mathematica
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155053
review text: The authors have discussed the concept of totally convex spaces in a series of papers. These are the Eilenberg-Moore algebras in the category of Banach algebras (with linear contractions as morphisms). This study is continued in the paper under review where they define a topology, the radial topology, on such spaces. They are particularly interested in the category of separated spaces. These are the objects of the regular epi- reflexive hull of the subcategory consisting of the unit balls of Banach spaces. In particular, they characterise the epi-morphisms in this subcategory. They also consider similar questions for the so-called finitely totally convex spaces which are essentially the ''non-complete'' analogues of totally convex spaces.
Mathematics Subject Classification ID: 46M99
Mathematics Subject Classification ID: 46A19
Mathematics Subject Classification ID: 18C20
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 3955758
zbMATH Keywords: totally convex spaces
zbMATH Keywords: Eilenberg-Moore algebras in the category of Banach algebras
zbMATH Keywords: radial topology
zbMATH Keywords: separated spaces
zbMATH Keywords: regular epi-reflexive hull
zbMATH Keywords: epi-morphisms
zbMATH Keywords: finitely totally convex spaces
reviewed by: James B. Cooper
MaRDI profile type: Publication
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OpenAlex ID: W2377281176
description: scientific article; zbMATH DE number 3955758