Topologically inseparable functions II: Infinitary case
type: Item
instance of: scholarly article
title: Topologically inseparable functions II: Infinitary case
zbMATH Open document ID: 1018.54009
published in: Semigroup Forum
publication date: 2003-03-18T00:00:00Z
review text: The present paper is the second of a two part paper. The author studies the set of all functions \(g:A\to A\) that are continuous for all topologies for which a function \(f:A\to A\) \((A\) is an infinite set) is continuous (while in the first paper the given set \(A\) is finite). The paper is divided in two main sections. In the first part the author restricts his attention to unary functions topologically inseparable from \(f\). In the last part the author studies the clone of finitary functions inseparable from \(f\). The main result of this paper is that if \(f\) is infinitary, then the set \(S(A,f)= \{g:A\to A:g\) is continuous for all topologies for which \(f\) is continuous\} coincides with the set which contains only the constant functions and the iterates of \(f\).
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 54H10
zbMATH DE Number: 1883937
zbMATH Keywords: orbit
zbMATH Keywords: cycle
zbMATH Keywords: length of cycle
zbMATH Keywords: unbounded orbit
zbMATH Keywords: totally bounded function
zbMATH Keywords: clone
zbMATH Keywords: inseparable
author: R. A. Lewin
reviewed by: Chariklia Konstadilaki
MaRDI profile type: Publication
full work available at URL: s002330010156
OpenAlex ID: W4255571515
DOI: 10.1007/S002330010156
description: scientific article; zbMATH DE number 1883937