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Proceedings of the American Mathematical Society

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

 
 

 

Disk-like products of $ \lambda $ connected continua. I, II


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 51 (1975), 448-452
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1975-0375255-8
MathSciNet review: 0375255
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Abstract: A continuum $ X$ is $ \lambda $ connected if each two of its points can be joined by a heteditarily decomposable subcontinuum of $ X$. We prove that continua $ X$ and $ Y$ are atriodic and hereditarily unicoherent when the topological product $ X \times Y$ is disk-like. From this result and a theorem of R. H. Bing's it follows that $ \lambda $ connected continua $ X$ and $ Y$ are arc-like if and only if $ X \times Y$ is disk-like.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0375255-8
Keywords: Chainable continua, snake-like continua, disk-like product, arc-like continua, lambda connectivity, hereditarily decomposable continua, fixed point property, arcwise connectivity, triod, unicoherence
Article copyright: © Copyright 1975 American Mathematical Society

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