Some category bases which are equivalent to topologies
type: Item
instance of: scholarly article
title: Some category bases which are equivalent to topologies
zbMATH Open document ID: 0678.54021
published in: Real Analysis Exchange
publication date: 1989-01-01T00:00:00Z
review text: A category base is a pair (X,\({\mathcal C})\) where \({\mathcal C}\) is a family of subsets of nonempty set X which satisfies certain general set theoretic conditions. This concept unites features of the topological theory of category with features of measure theory. Every topological space is a category base; and a general question is: which category bases are equivalent to topological spaces? This paper gives a sufficient condition for this to be true, and applies it to two examples. A special case is that (assuming CH) for any Hausdorff measure \(\mu\) on \({\mathbb{R}}^ n\), there exists a topology \({\mathcal T}\) on \({\mathbb{R}}^ n\) such that the \(\mu\)- measurable sets are precisely the sets with the Baire property with respect to \({\mathcal T}\).
Mathematics Subject Classification ID: 54E52
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 4111564
zbMATH Keywords: meager set
zbMATH Keywords: category base
zbMATH Keywords: Hausdorff measure
zbMATH Keywords: Baire property
author: K. Schilling
reviewed by: R. A. McCoy
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4111564