On feebly monotone and related classes of mappings
type: Item
instance of: scholarly article
title: On feebly monotone and related classes of mappings
zbMATH Open document ID: 0951.54031
DOI: 10.1016/S0166-8641(99)00033-4
author: Janusz J. Charatonik
published in: Topology and its Applications
publication date: 2000-12-26T00:00:00Z
review text: A mapping between continua is said to be feebly monotone provided whenever the range is the union of two proper subcontinua, their preimages are connected. These mappings and their relations to monotone, almost monotone, quasi-monotone, and weakly monotone mappings are studied. Further, the author investigates special properties of continua in relation to these various classes of mappings. Results of \textit{J. B. Fugate} and \textit{L. Mohler} [Colloq. Math. 28, 221-224 (1973; Zbl 0277.54006)] and \textit{T. Maćkowiak} [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 24, 335-339 (1976; Zbl 0337.54019)] on the invariance of irreducibility of continua, known for quasi-monotone mappings, are extended to feebly monotone mappings. Relations between unicoherence of continua and feebly monotone mappings are established and previous results of the author's concerning terminal subcontinua, in the sense of \textit{D. E. Bennett} and \textit{J. B. Fugate} [Continua and their non-separating subcontinua, Diss. Math. 149 (1977; Zbl 0354.54017)] are extended.
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54F55
zbMATH DE Number: 1475347
zbMATH Keywords: quasi-monotone mappings
zbMATH Keywords: feebly monotone mappings
reviewed by: Donald E. Bennett
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1475347