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

 

Certain continua in $ S\sp{n}$ of the same shape have homeomorphic complements


Author: Vo Thanh Liem
Journal: Trans. Amer. Math. Soc. 218 (1976), 207-217
MSC: Primary 57A15; Secondary 54C56
MathSciNet review: 0397737
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Abstract: As a consequence of Theorem 1 of this paper, we see that if X and Y are globally 1-alg continua in $ {S^n}\;(n \geqslant 5)$ having the shape of the real projective space $ {P^k}\;(k \ne 2,2k + 2 \leqslant n)$, then $ {S^n} - X \approx {S^n} - Y$. (For $ {P^1} = {S^1}$, this establishes the last case of such a result for spheres.) We also show that if X and Y are globally 1-alg continua in $ {S^n},n \geqslant 6$, which have the shape of a codimension $ \geqslant 3$, closed, $ 0 < (2m - n + 1)$-connected, PL-manifold $ {M^m}$, then $ {S^n} - X \approx {S^n} - Y$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0397737-0
PII: S 0002-9947(1976)0397737-0
Keywords: Stable end, H-cobordism, regular neighborhood, shape, globally 1-alg
Article copyright: © Copyright 1976 American Mathematical Society