Topologically inseparable functions I: Finitary case
type: Item
instance of: scholarly article
title: Topologically inseparable functions I: Finitary case
zbMATH Open document ID: 1018.54008
author: Oscar Cartagena
author: Osvaldo Rubilar
author: R. A. Lewin
published in: Semigroup Forum
publication date: 2003-03-18T00:00:00Z
full work available at URL: http://hdl.handle.net/10925/751
review text: The present paper is the first of two papers in which the authors study the following problem: Given a finite set \(A\) and a distinguished function \(f:A\to A\), what can we say about the set of all functions \(g:A\to A\) that are continuous for all topologies for which \(f\) is continuous? In their effort to answer the above problem, the authors prove a lot of interesting results and finally show the main result which is a characterization of the functions \(f\) such that this set is trivial, that is, contains only the constant functions and the iterates of \(f\).
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 54H10
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 1883936
zbMATH Keywords: semigroup
zbMATH Keywords: inseparable
zbMATH Keywords: orbit
zbMATH Keywords: cycle
zbMATH Keywords: branch of the orbit
zbMATH Keywords: length-\(f\)-cyclic function
reviewed by: Chariklia Konstadilaki
MaRDI profile type: Publication
OpenAlex ID: W2086785615
DOI: 10.1007/S002330010155
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description: scientific article; zbMATH DE number 1883936