Some generalizations of universal mappings
type: Item
instance of: scholarly article
title: Some generalizations of universal mappings
zbMATH Open document ID: 0908.54027
published in: Rocky Mountain Journal of Mathematics
publication date: 1999-03-16T00:00:00Z
full work available at URL: CONT27-4.html
review text: A mapping \(f: X\to Y\) is universal if for each mapping \(g:X\to Y\) there is a point \(x\) in \(X\) such that \(f(x)= g(x)\). The author defines several variations of the concept, as semi-universal, weakly universal and pseudo-universal mappings, and establishes relationships between these classes of mappings, the fixed point property, the span of continua and the Borsuk-Ulam theorem. Reviewer's remarks: Theorem 4 (the composition of semi-universal mappings is semi-universal) and Theorem 6 (each inessential mapping \(f:X\to S^1\) is semi-universal) are false. Theorem 6 should be replaced by: ``each inessential mapping \(f:X\to S^1\) is weakly universal''. An appropriate ``Errata'' has been sent to the journal by the author.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 1206694
zbMATH Keywords: semi-universal
zbMATH Keywords: weakly universal
zbMATH Keywords: span of continua
author: M. M. Marsh
reviewed by: Janusz J. Charatonik
MaRDI profile type: Publication
OpenAlex ID: W1998077240
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DOI: 10.1216/RMJM/1181071868
description: scientific article; zbMATH DE number 1206694