Engulfing continua in an 𝑛-cell

Tondra, Richard J.

doi:10.1090/S0002-9947-1971-0279788-5

Engulfing continua in an $n$-cell
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Trans. Amer. Math. Soc. 158 (1971), 465-479 Request permission

Abstract:

In this paper it is shown that there exist open connected subsets ${D_1},{D_2}$, and ${D_3}$ of an $n$-cell $E$ such that, if $C$ is any proper compact connected subset of $E$ and $C \subset U,U$ open, then there exists a homeomorphism $h$ of $E$ onto itself such that $C \subset h({D_i}) \subset U$ for some $i,1 \leqq i \leqq 3$.

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