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Proceedings of the American Mathematical Society

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

 

 

Hausdorff hypercubes which do not contain arcless continua


Author: Michel Smith
Journal: Proc. Amer. Math. Soc. 95 (1985), 109-114
MSC: Primary 54F20; Secondary 54B10
MathSciNet review: 796457
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Abstract: A Hausdorff arc is a compact connected Hausdorff space with exactly two noncut points. The finite product of a Hausdorff arc is called a Hausdorff hypercube. Suppose that $ X$ is a Hausdorff arc which is first countable at none of its points and $ n$ is a positive integer. We show that every nondegenerate subcontinuum of $ {X^n}$ contains a Hausdorff arc. Thus $ {X^n}$ contains no nondegenerate hereditarily indecomposable continuum.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0796457-9
Keywords: Hausdorff arc, nonmetric arc, indecomposable continua
Article copyright: © Copyright 1985 American Mathematical Society