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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Aposyndetic continua as bundle spaces


Author: James T. Rogers
Journal: Trans. Amer. Math. Soc. 283 (1984), 49-55
MSC: Primary 54F20; Secondary 54F50, 55R10
MathSciNet review: 735408
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Abstract: Let $ \mathcal{S}$ be the $ P$-adic solenoid bundle, and let $ \eta :X \to {S^1}$ be a map of the continuum $ X$ onto $ {S^1}$. The bundle space $ B$ of the induced bundle $ {\eta ^{ - 1}}\mathcal{S}$ is investigated. Sufficient conditions are obtained for $ B$ to be connected, to be aposyndetic, and to be homogeneous. Uncountably many aposyndetic, homogeneous, one-dimensional, nonlocally connected continua are constructed. Other classes of continua are placed into this framework.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0735408-3
PII: S 0002-9947(1984)0735408-3
Keywords: Continuum, homogeneous, aposyndetic, solenoid, universal curve, induced bundle
Article copyright: © Copyright 1984 American Mathematical Society