On \(\sigma\)-porous sets and Borel sets
type: Item
instance of: scholarly article
title: On \(\sigma\)-porous sets and Borel sets
zbMATH Open document ID: 0692.54024
DOI: 10.1016/0166-8641(89)90091-6
author: Luděk Zajíček
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The main result of the paper is the following: For any countable ordinal number \(\alpha\) there exists a Borel set \(C\subset R\) such that for each Borel set B of additive class \(\alpha\) the symmetric difference \(B\Delta\) C is not \(\sigma\)-porous. The proof is based on a ``well-parametrized'' uncountable family of pairwise disjoint non-\(\sigma\)-porous sets and the Lebesgue method of ``universal functions''. The Real Anal. Exch. is a good source for knowledge of \(\sigma\)-porous sets [especially in 13(1987- 88), 314-550 (1989; Zbl 0666.26003)].
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 26A21
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 4133100
zbMATH Keywords: Borel set
zbMATH Keywords: non-\(\sigma\)-porous sets
zbMATH Keywords: universal functions
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90091-6
OpenAlex ID: W1969734235
cites work: Q5569299
cites work: Continuous functions need not have \(\sigma\)-porous graphs
cites work: Q5541832
cites work: A note on the \(\sigma\)-ideal of \(\sigma\)-porous sets
cites work: Constructions of some non-\(\sigma\)-porous sets on the real line
cites work: Porosity and \(\sigma\)-porosity
description: scientific article; zbMATH DE number 4133100