Constructions from null set vs invariance of manifolds – a problem? Are manifolds neither created nor destroyed?

If number set and system can be constructed and built up from null set, then likewise for resultant continuum i.e. manifold? That is, resultant infinite orders have reciprocal infinitesimal orders, and hence manifolds. But wouldn’t the conjecture of invariance of manifold(s) (topological invariance) be a counter point to such construction (both mathematically and physically?) of a continuum i.e. manifold? Therefore if one has a manifold in a physical model, it would seem that one could not use the argument of an earlier stage of no manifold, and then a subsequent constructed manifold i.e. such as Big Expansion. That is, the complement of manifold does not give rise to manifold, in the domain of discourse i.e. non-manifold does not give rise to manifold. Mathematical Conjecture: manifolds are neither created nor destroyed; such as for pre-Big Bang, and for variant scenario of consideration of any manifold creation from null set, in SRM.  Also see https://sites.google.com/site/zankaon and MSM web page. TMM