Every real function is the sum of two extendable connectivity functions
type: Item
instance of: scholarly article
title: Every real function is the sum of two extendable connectivity functions
zbMATH Open document ID: 0847.26003
author: Yanyan Li
published in: Real Analysis Exchange
publication date: 1996-10-06T00:00:00Z
review text: A function \(F: \mathbb{R}^2\to \mathbb{R}\) is a \textit{connectivity function} if the graph of its restriction \(F|C\) to any connected \(C\subset \mathbb{R}^2\) is connected in \(\mathbb{R}^3\). A function \(f: \mathbb{R}\to \mathbb{R}\) is an \textit{extendable function} if there exists a connectivity function \(F: \mathbb{R}^2\to \mathbb{R}\) with \(f(x)= F(x, 0)\) for every \(x\in \mathbb{R}\). The author constructs an extendable function, whose graph is dense in \(R\times R\) and uses this example to prove that every real function from \(\mathbb{R}\) to \(\mathbb{R}\) can be written as the sum of two extendable functions.
reviewed by: Tomasz Natkaniec
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 878224
zbMATH Keywords: Darboux function
zbMATH Keywords: peripheral continuity
zbMATH Keywords: negligible set
zbMATH Keywords: connectivity function
zbMATH Keywords: extendable function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 878224