yayyy after learning repr. theory and group theory to become fluently in that the new topic would be learning algebraic geometry and topology :

Calabi–Yau manifold - Wikipedia

yepp lets delve to String theory definition sets later. 

since might be a baseline to utilize logical definitions of each univer'se physics framework system. 

one other tjhing i very wonder is the compactness property in our universe.

so this is an addition to why i wonder very much string theory again. 

as told before i do not consider it as even finite dimensional even if particle physics or physics behaves in 3d usually, that does not mean its 3d imho.  but the mathematical structure of voidness and the iterations which are like noncontinous iterations i mean for instance eigenvalue changes instantly happenstance. this mathematical structure that based on the universe regimen via its force dynamics there creates some effects which is noncontinous. 

so is it a hausdorf space in terms of existence and voidness? 

no its not hausdorf if we consider it as multiverse :)

in meditation it sometimes talked of voidness. the voidness always captivated me in terms of existence iterating it over it with compact wise iterations.  this instant jump of eigenvalues from one to other eigenvalue (Though in sme articles that they say in some cases its not instantaneous) of the underlying mathematical structure, shows that there there is some underlying system which creates this 3d force system and that theories like which tells about how it happens to be 3d in this multiverse regimen be very interesting.   to extrapolate of stuff in this universe regimen to how entirety could be type thinking in string theory. 

and that i guess everything is a field.  (even voidness) 

its very fascinating surely. -> 

e.g. higgs boson. etc etc. 

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hmm currently most curious query is: quantum algebra structures of hebbian systems of standard neural cell architecture.