Directed topological spaces and funcoids

I have researched relations between directed topological spaces and pair of funcoids. Here the first funcoid represents topology and the

A funcoid related to directed topological spaces

The following problem arose from my attempt to re-express directed topological spaces in terms of funcoids. Conjecture Let be the

Two equivalent conjectures

I have added to my book a short proof that the following two conjectures are equivalent: Conjecture for every reloids

A new conjecture

While writing my book I overlooked to consider the following statement: Conjecture for principal funcoid and a set of funcoids

A new theorem about generalized continuity

I had this theorem in mind for a long time, but formulated it exactly and proved only yesterday. Theorem for

A new easy theorem

I added a new easy to prove proposition to my book: Proposition An endofuncoid is -separable iff for every .

A vaguely formulated problem

Consider funcoid (restricted identity funcoids on Frechet filter on some infinite set). Naturally (where is the identity morphism). But it

A new mapping from funcoids to reloids

Less than a hour ago I discovered a new mapping from funcoids to reloids: Definition for every funcoid . Now