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*To*: zzdev@xxxxxxxxxx*Subject*: Re: [zzdev] Subspaces & ZZ versioning*From*: Antti-Juhani Kaijanaho <gaia@xxxxxx>*Date*: Wed, 27 Dec 2000 11:35:20 +0200*In-reply-to*: <3A478411.4B27CC31@xxxxxx>; from b.fallenstein@xxxxxx on Mon, Dec 25, 2000 at 06:29:54PM +0100*Mail-followup-to*: zzdev@xxxxxxxxxx*References*: <3A34009B.FB990E0@xxxxxx> <20001211015201.E18012@xxxxxxxxxxxxxx> <3A342176.B03A9B9F@xxxxxx> <20001211035226.B3587@xxxxxxxxxxxxxx> <3A3E67F4.3C00B087@xxxxxx> <20001219124905.A7717@xxxxxxxxxxxxxx> <3A41351B.BA16A23D@xxxxxx> <20001221111527.B29066@xxxxxxxxxxx> <3A425394.C54EF3AC@xxxxxx> <3A478411.4B27CC31@xxxxxx>*Sender*: Antti-Juhani Kaijanaho <ajk@xxxxxxxxxxx>

On 20001225T182954+0100, Benjamin Fallenstein wrote: > Oops, just realized you've defined "subspace" to mean something else... > funny enough, the only kind of "subspace selector" currently working is > what your definition would call the subspace generated by a single cell > with respect to some given dimensions. Anyway, what I meant is, as I > said, a set of cells and a set of connections between these cells. Actually, I now think we need to revisit those definitions. I can see at least two good definitions for a subspace: 1) Let Z be a ZigZag space. Z' is a subspace of Z iff * it is a ZigZag space * its set of cells is a subset of Z's set of cells * its set of connections is a subset of Z's set of connections 2) Let Z be a ZigZag space. Z' is a subspace of Z iff * it is a subspace of Z (by definition 1) and * if d is a dimension in Z' and there is a connection along d in Z', then for all cells c and c' in Z', if there is a connection from c to c' along d in Z, then there is a connection from c to c' along d. 1 is your def. 2 is an extension of my earlier def (instead of a set of dims defining the subspace, we have two disjoint set of dims, one for defining the closure, and another for including more connections; I've been calling these hard and soft dimensions in my sketches). Def 1 is nice also theoretically since it mirrors many other subspace definitions in mathematics. Def 2 seems more natural: you cannot arbitrarily remove connections from a rank where the cells are in the space. -- %%% Antti-Juhani Kaijanaho % gaia@xxxxxx % http://www.iki.fi/gaia/ %%%

**Follow-Ups**:**Re: [zzdev] Re: [zzdev] Subspaces & ZZ versioning***From:*Benjamin Fallenstein

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**Re: [zzdev] Re: [zzdev] Re: [zzdev] Nile***From:*Antti-Juhani Kaijanaho

**Subspaces & ZZ versioning***From:*Benjamin Fallenstein

**Re: [zzdev] Subspaces & ZZ versioning***From:*Benjamin Fallenstein

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