A note on the \(\sigma\)-ideal of \(\sigma\)-porous sets
type: Item
instance of: scholarly article
title: A note on the \(\sigma\)-ideal of \(\sigma\)-porous sets
zbMATH Open document ID: 0656.26001
author: Ireneusz Recław
published in: Real Analysis Exchange
publication date: 1987-01-01T00:00:00Z
review text: In this note we show that \(\gamma\)-sets of reals are \(\sigma\)-porous and there exists a family of cardinality of the continuum of disjoint non- \(\sigma\)-porous perfect sets. [A family \({\mathcal A}\) of open subsets of \(X\subseteq {\mathbb{R}}\) is an \(\omega\)-cover of X iff every finite subset of X is contained in an element of \({\mathcal A}\). A space X has the \(\gamma\)-property (X is a \(\gamma\)-set) iff for every \(\omega\)-cover \({\mathcal A}\) of X there exists a family \(\{D_ m:\) \(m\in \omega \}\subseteq {\mathcal A}\) such that \(X\subseteq \cup_{k}\cap_{m\geq k}D_ m.]\)
Mathematics Subject Classification ID: 26A03
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 4071241
zbMATH Keywords: \(\sigma\)-porous sets on the real line
zbMATH Keywords: \(\gamma\)-sets
zbMATH Keywords: disjoint non- \(\sigma\)-porous perfect sets
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4071241