\(T_ 1\) spaces over topological sites
type: Item
instance of: scholarly article
title: \(T_ 1\) spaces over topological sites
zbMATH Open document ID: 0544.18002
DOI: 10.1016/0022-4049(83)90017-8
published in: Journal of Pure and Applied Algebra
publication date: 1983-01-01T00:00:00Z
review text: This brief note provides an elegant way of showing that in topological toposes many spaces can be represented as sheaves of continuous functions into the appropriate formal space. A locale X is called \(T_ 1\) iff for all locale morphisms f,g: \(Y\to X\), \(f^*\leq g^*\) pointwise implies \(f=g.\) Let \({\mathcal E}\) be a topological topos, that is to say \({\mathcal E}\) is sheaves on a topological site C. Then, if X is a \(T_ 1\)-locale, the sheaf of X-models in \({\mathcal E}\) is represented by the sheaf \(Cts( ,X): C^{op}\to Sets\) of continuous X-valued morphisms.
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 54B30
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 3865535
zbMATH Keywords: sheaves of continuous functions
zbMATH Keywords: formal space
zbMATH Keywords: locale
zbMATH Keywords: topological topos
author: Michael Paul Fourman
reviewed by: K. I. Rosenthal
MaRDI profile type: Publication
full work available at URL: 0022-4049(83)90017-8
OpenAlex ID: W2067014004
cites work: Q3322099
cites work: Q5626908
description: scientific article; zbMATH DE number 3865535