Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Layers of components of $ \beta([0,1]\times {\bf N})$ are indecomposable


Author: Michel Smith
Journal: Proc. Amer. Math. Soc. 114 (1992), 1151-1156
MSC: Primary 54D40
DOI: https://doi.org/10.1090/S0002-9939-1992-1093605-4
MathSciNet review: 1093605
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We examine the structure of certain subcontinua of the Stone-Čech compactification of the reals. Let $ N$ denote the integers, let $ X = [0,1] \times N$, and let $ C$ be a component of $ {X^*} = \beta X - X$. It is known that $ C$ admits an upper semicontinuous decomposition $ G$ into maximal nowhere dense subcontinua of $ C$ so that $ C/G$ is a Hausdorff arc. The elements of $ G$ are called layers. It has been shown that the layers of $ C$ that contain limit points of a countable increasing or decreasing sequence of cut points of $ C$ are nondegenerate indecomposable continua (various forms of this fact have been proven by Bellamy and Rubin, Mioduszewski, and Smith). We show that all the layers of $ C$ are indecomposable.*


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D40

Retrieve articles in all journals with MSC: 54D40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1093605-4
Keywords: Stone-Čech compactifications, nonmetric continua, indecomposable continua
Article copyright: © Copyright 1992 American Mathematical Society