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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
MathSciNet review: 1093605
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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.*

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Keywords: Stone-Čech compactifications, nonmetric continua, indecomposable continua
Article copyright: © Copyright 1992 American Mathematical Society

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