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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Engulfing continua in an $n$-cell


Author: Richard J. Tondra
Journal: Trans. Amer. Math. Soc. 158 (1971), 465-479
MSC: Primary 54.78
DOI: https://doi.org/10.1090/S0002-9947-1971-0279788-5
MathSciNet review: 0279788
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Abstract: In this paper it is shown that there exist open connected subsets ${D_1},{D_2}$, and ${D_3}$ of an $n$-cell $E$ such that, if $C$ is any proper compact connected subset of $E$ and $C \subset U,U$ open, then there exists a homeomorphism $h$ of $E$ onto itself such that $C \subset h({D_i}) \subset U$ for some $i,1 \leqq i \leqq 3$.


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Keywords: Engulfing, continua, collaring, tapered collaring, domain equivalence, compact equivalence, domain rank
Article copyright: © Copyright 1971 American Mathematical Society