Continuous functions need not have \(\sigma\)-porous graphs
type: Item
instance of: scholarly article
title: Continuous functions need not have \(\sigma\)-porous graphs
zbMATH Open document ID: 0607.26005
author: James Foran
published in: Real Analysis Exchange
publication date: 1986-01-01T00:00:00Z
review text: The author gives an example of a continuous function \(f:[0,1]\to R\) whose graph is a non-\(\sigma\)-porous subset of the plane and has the Hausdorff dimension 2.
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28A75
zbMATH DE Number: 3981465
zbMATH Keywords: \(\sigma \)-porous graphs
zbMATH Keywords: continuous functions
zbMATH Keywords: non-\(\sigma \)-porous subset
reviewed by: Jan Stanisław Lipiński
MaRDI profile type: Publication
Recommended article: An absolutely continuous function with non-\(\sigma\)-porous graph
Recommended article: Graphs of continuous functions from \({\mathbb R}\) to \({\mathbb R}\) are not purely unrectifiable
Recommended article: Continuous functions with impermeable graphs
Recommended article: Q5255639
Recommended article: Q4304610
Recommended article: Porosity and continuous, nowhere differentiable functions
Recommended article: Irregular \(1\)-sets on the graphs of continuous functions
Recommended article: Q4244948
Recommended article: Q5882352
Recommended article: Q3780084
description: scientific article; zbMATH DE number 3981465