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?

I know that in the smooth category the following is true. There are at most countable many disjoint embedded moebius bands in euclidean 3-space. Is this also true in topological category?

I know that in the smooth category the following is true. There are at most countable many embedded moebious bands in euclidean 3-space. Is this also true in topological category?

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?