Taming compacta in 𝐸⁴

Walsh, John J.; Wright, David G.

doi:10.1090/S0002-9939-1982-0674098-9

Taming compacta in $E^{4}$
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by John J. Walsh and David G. Wright PDF

Proc. Amer. Math. Soc. 86 (1982), 646-648 Request permission

Abstract:

A compactum $X$ in Euclidean $4$-space ${E^4}$ is shown to be tame if its projection into ${E^3}$ is $1$-dimensional and if $\dim L \cap X \leqslant 0$ for each vertical line $L$ in ${E^4}$. An essential ingredient is the result due to J. L. Bryant and D. L. Sumners that a $1$-dimensional compactum in a $3$-dimensional hyperplane of ${E^4}$ is tame in ${E^4}$.

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