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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homogeneous continua in Euclidean $ (n+1)$-space which contain an $ n$-cube are locally connected


Author: Janusz R. Prajs
Journal: Trans. Amer. Math. Soc. 307 (1988), 383-394
MSC: Primary 54F25; Secondary 54C25, 57N35
MathSciNet review: 936823
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Abstract: We prove that each homogeneous continuum which topologically contains an $ n$-dimensional unit cube and lies in $ (n + 1)$-dimensional Euclidean space is locally connected.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0936823-9
PII: S 0002-9947(1988)0936823-9
Keywords: Continuum, embedding, Euclidean space, homogeneity, local connectedness
Article copyright: © Copyright 1988 American Mathematical Society