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Proceedings of the American Mathematical Society

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

 
 

 

Parallelizability revisited


Author: Otomar Hájek
Journal: Proc. Amer. Math. Soc. 27 (1971), 77-84
MSC: Primary 54.82; Secondary 34.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0271925-7
MathSciNet review: 0271925
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Abstract: A classical theorem (Antosiewicz and Dugundji) states that a dynamical system on a locally compact separable metric space is parallelizable if and only if it is dispersive. In this paper it is shown that separability may be omitted, and, under a further condition, local compactness weakened to local Lindelöfness. The crucial step consists in a purely topological characterization of complete instability.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0271925-7
Keywords: Dynamical systems, parallelizability, global sections, completely unstable systems, dispersive systems, local sections, wandering points, fiber bundles, cross-sections, paracompact locally Lindelöf spaces
Article copyright: © Copyright 1971 American Mathematical Society

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