A duality involving Borel spaces
type: Item
instance of: scholarly article
title: A duality involving Borel spaces
zbMATH Open document ID: 1154.06005
author: Partha Pratim Ghosh
author: Dharmanand Baboolal
published in: The Journal of Logic and Algebraic Programming
publication date: 2008-09-01T00:00:00Z
review text: A Borel space is a set together with a collection of subsets (called Borel subsets) which is closed under countable unions and complements. Borel maps are functions between the underlying sets the inverse images of which preserve Borel sets. The arising category is called the category of Borel spaces. Sobriety in this category is defined in a manner fairly akin to one of characterizations of sober topological spaces. The gist of the paper is in establishing a dual equivalence between sober Borel spaces and spatial Boolean \(\sigma\)-frames. Reviewer's remark: It appears that there is an inadvertent tautology in Corollary 3.4. Since the Euclidean space \(\mathbb R^n\) is a separable metric space, and any metric space is separable iff it is second countable, statements (1) and (2) of the corollary are subsumed by statement (3).
reviewed by: Themba Dube
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 06D50
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 5318671
zbMATH Keywords: Borel spaces
zbMATH Keywords: Boolean \(\sigma\)-frames
zbMATH Keywords: adjunction
MaRDI profile type: Publication
full work available at URL: j.jlap.2008.02.009
OpenAlex ID: W1981681703
cites work: Q3270120
cites work: Realcompact spaces and regular σ -frames
cites work: Q3736543
cites work: Linear functionals on spaces of continuous functions
cites work: Atomless Parts of Spaces.
cites work: Q3965241
cites work: Q5639839
cites work: \(\kappa\)-frames
DOI: 10.1016/J.JLAP.2008.02.009
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description: scientific article; zbMATH DE number 5318671