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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weak chainability of pseudocones
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by David P. Bellamy PDF
Proc. Amer. Math. Soc. 48 (1975), 476-478 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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