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 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 , . Second, we show that in case of 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}
}