Talk:Coarse structure

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Anybody wanting to help with formatting of coarse structure is welcome: I only became a Wikipedia member today!

Controlled sets are not negligible: one can have controlled sets of arbitrarily large size when compared with X × X, and so they do not in general form an ideal set either.

I have reverted these changes as I do not see how they can be true generally.Xantharius (talk) 02:41, 8 September 2008 (UTC)Reply

The article says that ${\displaystyle \mathbb {Z} ^{n}}$ is coarsely equivalent to the n-dimensional euclidean space, but it doesn't say what "coarse equivalence" is. The usual ad hoc approach declaring some functions to be morphisms and use the standard categorial definition for "isomorphism" doesn't work here because any such isomorphism would be a bijection between ${\displaystyle \mathbb {Z} ^{n}}$ and ${\displaystyle \mathbb {R} ^{n}}$.

So what is the precise definition of "coarsely equivalent" ? Is there a concept of "coarse morphisms" ? How are they defined? Perhaps as certain equivalence classes of functions as for the homotopy-categories? 84.139.131.35 (talk) 18:30, 1 October 2009 (UTC)Reply