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• CommentRowNumber1.
• CommentAuthorporton
• CommentTimeJul 30th 2016

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?

• CommentRowNumber2.
• CommentAuthorporton
• CommentTimeJul 30th 2016
• (edited Jul 30th 2016)

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?

• CommentRowNumber3.
• CommentAuthorporton
• CommentTimeJul 31st 2016

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.