I present my mathematical theory of singularities. It may probably have applications in general relativity and other physics.
The definitions are presented in this short draft article.
Before reading this article I recommend to skim through my research monograph (in the field of general topology), because the above mentioned article uses concepts defined in my book.
In short: I have defined “meta-singular numbers” which extend customary (real, complex, vector, etc.) numbers with values which functions take at singularities. If we allow meta-singular solutions of (partial) differential equations (such as general relativity) the equations remain the same, but the meaning of them changes. As such, we may probably get a modified version of general relativity and other theories.
Please collaborate with me to apply my theory to general relativity (I am no expert in relativity) and share half of Nobel Prize with me (if the results will be interesting, what I don’t 100% warrant now).
Anyway, we now have an interesting topic of research: What’s about solutions of differential equations in terms of meta-singular numbers?
Ugh, error:
The singularity level above in not $latex T_2$-separable. Thus descending from upper singularity levels to lower levels (such as real numbers) is not properly defined.
Goodbye Nobel Prize.
I’ve reverted to a previous messy informal version of this article, because my later formalization was an error.