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From the definition of directed topological space it follows that the unit circle with $2n$ circumference clockwise paths ($n\in\mathbb{N}$) is a d-space.
This d-space is “nonlocal” that is not determined by small fragments of the path.
“Regular” clockwise circle with $n$ circumference clockwise paths ($n\in\mathbb{N}$) is a d-space too. And this one is “local”.
I ask you to help me define “locality” or “nonlocality” of d-spaces. What is the definition and how is it called?
Possible definition of locality:
From every non-constant d-path we can “extract” a non-constant simple d-path which is its subpath.
Does this definition conform to the intuition about (non)locality?
Sorry, completely wrong:
I was pointed that the unit circle with $2n$ circumference clockwise paths is not a d-space, because from every path a shorter path can be extracted.
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