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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A new subcontinuum of $\beta \mathbb{R}\setminus \mathbb{R}$


Authors: Alan Dow and Klaas Pieter Hart
Journal: Proc. Amer. Math. Soc. 125 (1997), 1861-1871
MSC (1991): Primary 54D40, 54F15; Secondary 04A30, 54G05
MathSciNet review: 1415584
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Abstract | References | Similar Articles | Additional Information

Abstract: We present a method for describing all indecomposable subcontinua of $\beta \mathbb{R}\setminus \mathbb{R}$. This method enables us to construct in $\mathsf {ZFC}$ a new subcontinuum of $\beta \mathbb{R}\setminus \mathbb{R}$.

We also show that the nontrivial layers of standard subcontinua can be described by our method. This allows us to construct a layer with a proper dense $F_\sigma $-subset and bring the number of (known) nonhomeomorphic subcontinua of $ \beta \mathbb{R}\setminus \mathbb{R}$ to 14.


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Additional Information

Alan Dow
Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
Email: dowa@mathstat.yorku.ca

Klaas Pieter Hart
Affiliation: Faculty of Technical Mathematics and Informatics, TU Delft, Postbus 5031, 2600 GA Delft, The Netherlands
Email: k.p.hart@twi.tudelft.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04055-0
PII: S 0002-9939(97)04055-0
Keywords: Continuum, indecomposable continuum, shift on~$\omega^*$, Continuum Hypothesis
Received by editor(s): December 17, 1995
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1997 American Mathematical Society



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