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From Dirk-Willem van Gulik <di...@webweaving.org>
Subject Re: A mathematical vision of XML leads to interesting conclusions
Date Mon, 20 Dec 1999 10:29:33 GMT


On Sat, 18 Dec 1999, Brett McLaughlin wrote:

> > If you think about it, the namespace idea is the real key to XML
> > success: namespaces are "versors" of an "infinite-dimension" solution
> > space. Topologically speaking, while SGML is an single infinite
> > dimension, XML is an infinite set of infinite dimensions. Mathematically
> > speaking, you can create a one to one relationship with all the points
> > of XML to SGML (like it's done considering, for example,
> > "xsl:stylesheet" like a one dimensional SGML element, rather than the
> > "stylesheet" element of the "xsl" namespace). This may lead to imply
> > that SGML and XML have the same "multidimentional" volume. Thus,
> > namespaces don't alter the topological tissue of XML (which remains flat
> > and one-dimentional), but simply adds "classes" of elements to allow
> > elements to share the same name, but have different meanings.

Having given this more though; I still fail to see topology here. I can
imagine how you can model this as transformations on set's, even see how a
graaf would fit. But topology no. Meanwhile of course, this looks a lot
like those 'Architectural Form's. Which never went anywhere.

Dw



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