A new subcontinuum of $\beta \mathbb {R}\backslash \mathbb {R}$
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- by Alan Dow and Klaas Pieter Hart PDF
- Proc. Amer. Math. Soc. 125 (1997), 1861-1871 Request permission
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.References
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Additional Information
- Alan Dow
- Affiliation: Department of Mathematics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
- MR Author ID: 59480
- 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
- Received by editor(s): December 17, 1995
- Communicated by: Franklin D. Tall
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1861-1871
- MSC (1991): Primary 54D40, 54F15; Secondary 04A30, 54G05
- DOI: https://doi.org/10.1090/S0002-9939-97-04055-0
- MathSciNet review: 1415584