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*To*: Antti-Juhani Kaijanaho <gaia@xxxxxx>, ZZ Development <zzdev@xxxxxxxxxx>*Subject*: Scribbles*From*: Benjamin Fallenstein <b.fallenstein@xxxxxx>*Date*: Wed, 27 Dec 2000 14:37:15 +0100

Hi A-J! I've read your scribbles, and I think I understood them (except: what is an injection?). Dom d is the X' from your theorem section, i.e. the set of cells which have posward connections along d, right? Mostly, it makes sense, just the last section is problematic. The important thing about clone dimensions is not simply that the contents are equal; the important thing is they *stay* equal. I.e., I'd say: If d is a clone dimension, then for all ZigZag spaces Z = (X, c, C) for which d element of X, it holds for every x element of Dom d in that space that c(x) = c(Dim{d}(x)). (By your definition, not only all dimensions where cells have the same content by chance would be clone dimensions, but also *all cells not used as dims*! So, each non-dimension cell would be a clone dimension ;).) - Benja

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