It was my long time dream since the first course of the university to do math analysis in algebraic fashion instead of the notorious epsilon-delta notation overloaded with quantifiers.
This dream has been accomplished. I discovered a new math theory in which I call Algebraic General Topology in the field of General Topology.
It all plays math nicely (except of the fact that I’ve found many open problems which are not yet solved).
But today I stumbled over a principal difficulty which is probably is some kind of end of my successful research where I nicely express all in algebraic formulas:
This is an alternative definition of product of uniform spaces. It is essentially non-algebraic and uses lots of words and quantifiers. And when I thought how to simplify it in terms of Algebraic General Topology I found that there are no (at least no obvious) simplification of this definition using my theory.
I feel somehow sad about this.
I call you to participate in this research and find a way to study it in an algebraic way. Probably category theory can help. Please write me if you want to do the research together with me.