Atriodic homogeneous continua
type: Item
instance of: scholarly article
title: Atriodic homogeneous continua
zbMATH Open document ID: 0554.54019
author: C. L. Hagopian
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The paper contains a classification of atriodic homogeneous continua. Every such continuum is either a solenoid, or a hereditarily indecomposable continuum, or it has a continuous decomposition to a solenoid with layers homeomorphic to the same hereditarily indecomposable homogeneous continuum. According to Roger's result, every hereditarily indecomposable homogeneous continuum is tree-like. Therefore, in particular, it is obtained that an atriodic homogeneous continuum is 1- dimensional (the answer to a question of \textit{T. Maćkowiak} and \textit{E. D. Tymchatyn} [Diss. Math. 225 (1984; Zbl 0584.54029)]. If every tree-like homogeneous continuum is a pseudo-arc (this is unknown), then, by the above classification theorem, the following continua form a full list of atriodic homogeneous continua: solenoids, the pseudo-arc, the solenoids of pseudo-arcs (analogously in the plane we will have only the following nondegenerate homogeneous continua: the circle, the pseudo-arc, the circle of pseudo-arcs).
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54F50
Mathematics Subject Classification ID: 54H15
zbMATH DE Number: 3883188
zbMATH Keywords: atriodic homogeneous continua
zbMATH Keywords: hereditarily indecomposable continuum
zbMATH Keywords: decomposition
zbMATH Keywords: 1-dimensional
zbMATH Keywords: solenoids
zbMATH Keywords: pseudo-arc
reviewed by: Tadeusz Maćkowiak
MaRDI profile type: Publication
full work available at URL: pjm.1984.113.333
OpenAlex ID: W1970382666
DOI: 10.2140/PJM.1984.113.333
description: scientific article; zbMATH DE number 3883188