Using “compactness of funcoids” which I defined earlier, I’ve attempted to generalize the classic general topology theorem that compact topological spaces and uniform spaces bijectively correspond to each other.
I’ve resulted with the theorem
Theorem Let is a -separable (the same as for symmetric transitive) compact funcoid and is an reflexive, symmetric, and transitive endoreloid such that . Then .
But wait, reflexive, symmetric, and transitive endoreloid is practically the same as a uniform space.
So my theorem is about uniform spaces, just like as the classic theorem. I haven’t succeeded to generalize, I’ve just formulated and proved the same classical well known theorem.
A sad for me conclusion: My theory has not added value for the case of compact spaces. In this case my theory just coincides with classic general topology.