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I created the article coarse structure.
Thanks for all these additions!
May I suggest some edit hints?
At coarse structure I have made more of the keywords into hyperlinks (and I have added a parenthetical explanation of ). The idea is to make the page as useful as possible by providing the reader with pointers to all relevant background information.
Then I added under “Related entries” a pointer to bornological closed structure, thus cross-referencing the two entries. The idea here is to give the reader the chance to find further information without them already knowing what they might be looking for.
Finally, I gave bornological coarse space and motovic coarse space redirects to the plurals of their titles. On the one hand it is good to add plural redirects to every entry by default anyway, on the other hand some of your other entries were indeed already trying to point to these plurals. Now the links work.
There are more edits along these lines that could be done to your other additons. I’ll stop here, I suppose you see the point. It’s a tad more work to add all this cross-linking and redirecting, but it helps ensure that the material one adds will actually find users.
Thanks!
I wonder how this coarse bornology account fits with the nPOV of space. I was left from our conversation on bornological sets wanting to know more, such as whether there was a form of cohesion around, and expecting great things from .
Then there’s some form of localization at interval, as in -homotopy. I remember Urs and Ben-Zvi on the latter fitting in with the DAG outlook.
A coarse structure looks suspiciously similar to that on a uniform space, though somewhat weaker.
I assume it was relational compositions (and relational inverses) that was meant, so I stuck that in.
Yes, it’s relational composition (are there any others?).
Entourages in a uniform structure are closed under taking supersets, which is pretty much the opposite of what the definition of a coarse structure wants.
However, it is possible to define coarse uniform spaces, see Definition 5.3 in Bunke and Engel, which have compatible coarse and uniform structures.
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