English

Pairwise disjoint Moebius bands in space

Geometric Topology 2022-12-07 v1 General Topology

Abstract

V.V.Grushin and V.P.Palamodov proved in 1962 that it is impossible to place in R3R^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 RNR^N, N3N\geqslant 3. Second, we show that in case of R3R^3 the theorem holds for arbitrarily topologically embedded (not necessarily tame) Moebius bands.

Cite

@article{arxiv.2212.02983,
  title  = {Pairwise disjoint Moebius bands in space},
  author = {Olga Frolkina},
  journal= {arXiv preprint arXiv:2212.02983},
  year   = {2022}
}
R2 v1 2026-06-28T07:23:35.348Z