Proceedings of the American Mathematical Society

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



Mapping cylinder neighborhoods in the plane

Authors: Beverly Brechner and Morton Brown
Journal: Proc. Amer. Math. Soc. 84 (1982), 433-436
MSC: Primary 57N05; Secondary 54F25, 57N60
MathSciNet review: 640248
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Abstract: We characterize those compact subsets of the plane which have mapping cylinder neighborhoods, describe the neighborhood closures, and show that such neighborhood closures are topologically unique. The proofs employ the notion of prime ends. We also show that if $ U$ is a mapping cylinder neighborhood of a pointlike continuum in $ {S^3}$, then $ \overline U $ is a $ 3$-cell.

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Keywords: Mapping cylinder neighborhood, prime ends, plane homeomorphisms
Article copyright: © Copyright 1982 American Mathematical Society