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Cut points in Čech-Stone remainders


Authors: Alan Dow and Klaas Pieter Hart
Journal: Proc. Amer. Math. Soc. 123 (1995), 909-917
MSC: Primary 54D40; Secondary 03E50, 54A35, 54F15, 54F50
DOI: https://doi.org/10.1090/S0002-9939-1995-1216810-5
MathSciNet review: 1216810
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Abstract: We investigate cut points of subcontinua of $ \beta \mathbb{R}\backslash \mathbb{R}$. We find, under CH, the topologically smallest type of subset of $ \mathbb{R}$ that can support such a cut point. On the other hand we answer Question 66 of Hart and van Mill's Open problems on $ \beta \omega $ [Open Problems in Topology (J. van Mill and G. M. Reed, eds.), North-Holland, Amsterdam, 1990, pp. 97-125] by showing that it is consistent that all cut points are trivial (in a sense to be made precise in the paper).


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1216810-5
Keywords: Čech-Stone compactification, continuum, cut point, Laver forcing
Article copyright: © Copyright 1995 American Mathematical Society

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