A characterization of extendable connectivity functions
type: Item
instance of: scholarly article
title: A characterization of extendable connectivity functions
zbMATH Open document ID: 0638.26004
author: Richard G. Gibson
author: Fred Roush
published in: Real Analysis Exchange
publication date: 1988-01-01T00:00:00Z
review text: Let \(f: I\to I\) be a function where \(I=[0,1]\). In this paper a family of peripheral intervals for f is defined and the following theorems are proved. Theorem 1. If a family of peripheral intervals exists for \(f: I\to I\), then f is the restriction of a connectivity function g: I \(2\to I\) such that g is continuous on the complement of \(I\times 0\) where I is embedded in I 2 as \(I\times 0.\) Theorem 2. The existence of a family of peripheral intervals is both necessary and sufficient that a function \(f: I\to I\) be the restriction of a connectivity function g: I \(2\to I\) where I is embedded in I 2 as \(I\times 0\).
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54C20
zbMATH DE Number: 4040199
zbMATH Keywords: peripheral intervals
zbMATH Keywords: connectivity function
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4040199