A tensor-hom adjunction in a topos related to vector topologies and bornologies
type: Item
instance of: scholarly article
title: A tensor-hom adjunction in a topos related to vector topologies and bornologies
zbMATH Open document ID: 0966.18003
DOI: 10.1016/S0022-4049(99)00188-7
author: Luis Español
author: Laureano Lambán
published in: Journal of Pure and Applied Algebra
publication date: 2001-08-12T00:00:00Z
review text: Let \(\mathcal{M}\) be the topos of \(M\)-sets, where \(M\) is the monoid of continuous maps \(f:N\rightarrow N\) such that \(f(\infty)=\infty \), \(N=\mathbb{N}\) \(\cup \left\{ \infty \right\} \) being the one point compactification of the discrete space of natural numbers. This topos is used as a universe of presheaves, and the sheaf subtoposes \(\mathcal{C}\) (called continuous topos, and adapted from Johnstone' s topological topos) and \(\mathcal{B}\) (called bounded topos, and adapted from Lawvere' s bornological topos) are introduced and studied. A tensor-hom adjunction between certain categories of modules (over the ring of continuous reals, respectivelly bounded reals in \(\mathcal{M}\)) in \(\mathcal{C}\), respectively in \(\mathcal{B}\) is constructed. Finally, using the above construction, an adjunction between adequate categories of topological and bornological real vector spaces is obtained.
reviewed by: I. Tofan
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 46A17
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 1538802
zbMATH Keywords: compactification
zbMATH Keywords: continuous topos
zbMATH Keywords: bornological topos
zbMATH Keywords: universe of presheaves
zbMATH Keywords: topological real vector spaces
MaRDI profile type: Publication
cites work: On Sequential Convergence
cites work: Q4040131
cites work: Q4132979
cites work: Q4145861
cites work: On a Topological Topos
cites work: Q4204315
cites work: Convergence du type L
cites work: Q3792854
cites work: Sheaves in geometry and logic: a first introduction to topos theory
Wikidata QID: Q128055026
description: scientific article; zbMATH DE number 1538802