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MR943307 (90f:54055) 54F20 (57N35)
Prajs, Janusz R. Homogeneous continua in Euclidean $(n+1)$-space which contain an $n$-cube are $n$-manifolds. Trans. Amer. Math. Soc. 318 (1990), no. 1, 143–148.
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