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Geometric taming of compacta in $ E\sp{n}$


Author: David G. Wright
Journal: Proc. Amer. Math. Soc. 86 (1982), 641-645
MSC: Primary 57N35; Secondary 57N15, 57N45, 57N75
DOI: https://doi.org/10.1090/S0002-9939-1982-0674097-7
MathSciNet review: 674097
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Abstract: We investigate $ k$-dimensional compacta in $ {E^n}(k \leqslant n - 3)$ that satisfy geometric properties. We prove that such a compactum $ X$ in $ {E^n}$ is tamely embedded if each point of $ X$ can be touched by the tip of a cone from the complement of $ X$. Furthermore, we show that a $ k$-dimensional compactum $ Y$ in $ {E^n}(k \leqslant n - 3)$ is tame if $ Y$ has vertical order $ n - k - 2$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0674097-7
Keywords: Tame embeddings, vertical order, topological embeddings of compacta
Article copyright: © Copyright 1982 American Mathematical Society

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