I know that in the smooth category the following is true. There are at most countable many embedded moebius bands in euclidean 3-space. Is this also true in topological category?
There are at most countably many disjoint embeddings of homeomorphic images of a non-orientable hypersurface in $\mathbb R^k$. This is theorem 2 in "An uncountable family of disjoint spatial continua in Euclidean space" by V.K. Ionin and Yu.G. Nikonorov.