Before revision:  We show that separability of such spaces or their subspaces has very strong implications in terms of  dominatedness of the set of priors and thus for applications in the field of robust finance.
After revision:  We show that separability of such spaces or their subspaces has very strong implications in terms of dominatedness of the set of priors and the lack of order completeness. Our results have subtle implications for the field of robust finance.