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Proceedings of the American Mathematical Society

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

 
 

 

Weak chainability of pseudocones


Author: David P. Bellamy
Journal: Proc. Amer. Math. Soc. 48 (1975), 476-478
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1975-0365515-9
MathSciNet review: 0365515
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Abstract: A pseudocone over $ X$ is a compactification of $ (0, 1]$ with remainder $ X$. $ S$ is a circle. A characterization of those pseudocones over $ S$ which are weakly chainable is given. (A continuum is weakly chainable if and only if it is a continuous image of the pseudoarc.) Covering projections and liftings are used, and a simple geometric interpretation of the result is that a pseudocone over $ S$ is weakly chainable if and only if the absolute value of the winding number of any subarc of $ (0, 1]$ around $ S$ is bounded by some $ m > 0$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0365515-9
Keywords: Compactification, covering projection, chainable continuum
Article copyright: © Copyright 1975 American Mathematical Society

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