On indecomposable subcontinua of \(\beta{}[0,\infty{})-[0,\infty{})\)
type: Item
instance of: scholarly article
title: On indecomposable subcontinua of \(\beta{}[0,\infty{})-[0,\infty{})\)
zbMATH Open document ID: 0753.54016
DOI: 10.1016/0166-8641(92)90008-N
published in: Topology and its Applications
publication date: 1993-01-16T00:00:00Z
review text: The remainder in the Stone-Čech compactification \(\beta(N\times I)\), where \(N\) is the set of positive integers and \(I\) is the closed (unit) interval of reals, \(0\leq t\leq 1\), both with usual topologies, is a union of continua \(M\) indexed by points of the remainder in the Stone-Čech compactification \(\beta N\), which are irreducible between points in \(\beta(N\times \{0\})\) and \(\beta(N\times \{1\})\) and have decompositions into layers with the quotient spaces being Hausdorff arcs. The author shows that all the layers in continua \(M\) are indecomposable and that among remote layers there exist non-degenerate ones. This answers questions of the reviewer [Topology and Measure, Part 2, Conf. Zinnowitz 1974, 257-283 (1978; Zbl 0407.54018)]. Assuming new axioms consistent with ZFC, the author shows that there are infinitely many non- homeomorphic indecomposable continua in the remainder of \(\beta(N\times I)\), in particular, continuum many if there is an inaccessible cardinal.
reviewed by: Jerzy Mioduszewski
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54D40
Mathematics Subject Classification ID: 03E25
zbMATH DE Number: 90162
zbMATH Keywords: Stone-Čech compactification
zbMATH Keywords: indecomposable continua
author: Jian-Ping Zhu
MaRDI profile type: Publication
cites work: A non-metric indecomposable continuum
cites work: Q3784821
cites work: Countable ultraproducts without CH
cites work: Non-isomorphic hyper-real fields from non-isomorphic ultrapowers
cites work: Q3782430
full work available at URL: 0166-8641(92)90008-n
OpenAlex ID: W2061786198
description: scientific article; zbMATH DE number 90162