Yesterday I asked this question following the thought that an inner structure of spacetime can be embraced in a structure function $s(x)$, to allow for a field theory with macroscopically curved background that is also microscopically nontrivial.
This is a problematic question because the concept "inner structure" of spacetime was not well-defined by me; I don't have this concept more than at the level of an image or intuition. Also the field theory I was referring to is not explicated: I didn't give an expression for $\mathscr{L}$, because interested only on $s$.
I still want to ask this question, because I desire to know about the subject of spacetime topology (maybe is a more correct term), so how can it be asked, considering the intrinsic ignorance of who's asking? How can it be made more clear or detailed?