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Proceedings of the American Mathematical Society

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

 
 

 

Torus-like products of $ \lambda $ connected continua


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 53 (1975), 227-230
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1975-0385818-1
MathSciNet review: 0385818
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Abstract: Recently the author [5] proved that $ \lambda $ connected continua $ X$ and $ Y$ are arc-like if and only if the topological product $ X \times Y$ is disklike. Here we present an analogous theorem that generalizes the result of Fort [2] and Ganea [3] that disks are not torus-like. We prove that $ \lambda $ connected continua $ X$ and $ Y$ are circle-like if and only if $ X \times Y$ is torus-like.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0385818-1
Keywords: Circle-like continua, torus-like product, lambda connected continua, hereditarily decomposable continua, triod, unicoherence, $ \epsilon $-mappings onto a torus
Article copyright: © Copyright 1975 American Mathematical Society

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