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 second one represents direction.

Results are mainly negative:

Not every directed topological space can be represented as a pair of funcoids.

Different pairs of a topological space and its subfuncoid may generate the same directed topological space.

The research is currently available here. See also my book.

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