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Concerning the shapes of finite-dimensional compacta


Authors: Ross Geoghegan and R. Richard Summerhill
Journal: Trans. Amer. Math. Soc. 179 (1973), 281-292
MSC: Primary 54C56
DOI: https://doi.org/10.1090/S0002-9947-1973-0324637-1
MathSciNet review: 0324637
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Abstract: It is shown that two ``tamely'' embedded compacta of dimension $ \leq k$ lying in $ {E^n}(n \geq 2k + 2)$ have the same (Borsuk) shape if and only if their complements are homeomorphic. In particular, two k-dimensional closed submanifolds of $ {E^{2k + 2}}$ have the same homotopy type if and only if their complements are homeomorphic.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0324637-1
Article copyright: © Copyright 1973 American Mathematical Society

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