Pairwise disjoint Moebius bands in space

Olga Frolkina

doi:10.1142/s0218216518420051

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arXiv · 2212.02983

Pairwise disjoint Moebius bands in space

Olga Frolkina

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Abstract

V.V.Grushin and V.P.Palamodov proved in 1962 that it is impossible to place in $R^3$ uncountably many pairwise disjoint polyhedra each homeomorphic to the Moebius band. We generalize this result in two directions. First, we give a generalization of this result to tame subsets in $R^N$, $N\geqslant 3$. Second, we show that in case of $R^3$ the theorem holds for arbitrarily topologically embedded (not necessarily tame) Moebius bands.

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Olga Frolkina. 2022-12-05. Pairwise disjoint Moebius bands in space. https://doi.org/10.1142/s0218216518420051

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