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Re: [zzdev] Subspaces & ZZ versioning
- 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
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/ %%%