Geometric taming of compacta in 𝐸ⁿ

Wright, David G.

doi:10.1090/S0002-9939-1982-0674097-7

Geometric taming of compacta in $E^{n}$
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Proc. Amer. Math. Soc. 86 (1982), 641-645 Request permission

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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