Some Conjectures About Generalized Limits
Continuing my research from general topology monograph Algebraic General Topology, the following new open problems arose: I remind that I define generalized limit of arbitrary function. This limit is defined in terms of funcoids. As I show in the Book 3, Algebra, generalized limit is defined for generalized spaces, for example for reloids. So, how […]
Product of compact funcoids is compact
I have proved (for any products, including infinite products): Product of directly compact funcoids is directly compact. Product of reversely compact funcoids is reversely compact. Product of compact funcoids is compact. The proof is in my draft article and is not yet thoroughly checked for errors.
The end of Algebraic General Topology?
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 […]