Extremal continua: A class of non-separating subcontinua
type: Item
instance of: scholarly article
title: Extremal continua: A class of non-separating subcontinua
zbMATH Open document ID: 0598.54016
DOI: 10.1016/0166-8641(85)90043-4
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The notion of a terminal continuum, as defined by \textit{D. E. Bennett} and \textit{J. B. Fugate} [Diss. Math. 149 (1977; Zbl 0354.54017)] is used to introduce extremal continua, a class of non-separating subcontinua of a continuum. An extremal continuum can be characterized as a proper subcontinuum Y of a metric continuum x with the property that Y contains a point of irreducibility of each irreducible subcontinuum of X that meets Y. If Y is an extremal subcontinuum of X, then Y does not separate any subcontinuum of X containing Y; moreover, if Y is a proper subcontinuum of X and Y does not cut any subcontinuum of X containing Y, then Y is extremal in X.
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 3964962
zbMATH Keywords: absolutely non-cutting subcontinuum
zbMATH Keywords: non-cutting subcontinuum
zbMATH Keywords: absolutely non-separating subcontinuum
zbMATH Keywords: end point in the classical sense
zbMATH Keywords: extremal subcontinuum
zbMATH Keywords: continuumwise connectedness
zbMATH Keywords: terminal continuum
zbMATH Keywords: extremal continua
zbMATH Keywords: non-separating subcontinua
zbMATH Keywords: point of irreducibility
author: Margaret Ann Owens
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90043-4
OpenAlex ID: W2072966759
cites work: Q4125467
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cites work: Q3304890
cites work: On plane dendroids and their end points in the classical sense
cites work: On Unicoherent Continua
cites work: Q5517570
description: scientific article; zbMATH DE number 3964962