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1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeJul 30th 2016
   • PermaLink
   Author: porton
   Format: MarkdownItexFrom the definition of [directed topological space](https://ncatlab.org/nlab/show/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?

   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?

2. • CommentRowNumber2.
   • CommentAuthorporton
   • CommentTimeJul 30th 2016
   • (edited Jul 30th 2016)
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   Author: porton
   Format: MarkdownItexPossible 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?

   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?

3. • CommentRowNumber3.
   • CommentAuthorporton
   • CommentTimeJul 31st 2016
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   Author: porton
   Format: MarkdownItexSorry, 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.

   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.