The coproduct of totally convex spaces
type: Item
instance of: scholarly article
title: The coproduct of totally convex spaces
zbMATH Open document ID: 0619.46063
author: Dieter Pumplün
author: Helmut Röhrl
published in: Beiträge zur Algebra und Geometrie
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/138373
review text: The functor \({\hat 0}\) from the category \(Ban_ 1\) to the category TC of totally convex spaces has a left adjoint S. It is shown that S in turn has a left adjoint. This fact allows the description of the coproduct in a very special case and leads to the definition of the direct sum of objects in TC. The direct sum turns out to be the coproduct for separated totally convex spaces. In addition, it gives an explicit description of the interior of the coproduct in the general case. The description of the boundary of the coproduct is given by an explicit construction. Additionally, the authors investigate which of the interesting subcategories of TC are closed under coproducts and which of the results on coproducts remain valid for the category of finitely totally convex spaces.
Mathematics Subject Classification ID: 46M15
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 18A30
zbMATH DE Number: 4004954
zbMATH Keywords: functor
zbMATH Keywords: left adjoint
zbMATH Keywords: coproduct
zbMATH Keywords: coproduct for separated totally convex spaces
MaRDI profile type: Publication
Recommended article: Coproducts of proximity spaces
Recommended article: Coincidence theorems in product \(G\)-convex spaces
Recommended article: Q3970623
Recommended article: Q3766290
Recommended article: Normed totally convex spaces
Recommended article: A general theory of tensor products of convex sets in Euclidean spaces
Recommended article: Q4894768
Recommended article: Convex compact spaces and their maps
Recommended article: Complements of convex topologies on products of finite totally ordered spaces
Recommended article: Q4840131
description: scientific article; zbMATH DE number 4004954