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Transactions of the American Mathematical Society
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
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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PII: S 0002-9947(1971)0279788-5
Keywords: Engulfing, continua, collaring, tapered collaring, domain equivalence, compact equivalence, domain rank
Article copyright: © Copyright 1971 American Mathematical Society