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Date: Thu, 4 Nov 2004 00:06:20 +0000
From: Martin Bays <jboste@zugzwang.port5.com>
To: lojban-list@lojban.org
Subject: [lojban] Re: how to say manifold
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* Wednesday, 2004-11-03 at 19:20 -0400 - Pierre Abbat <phma@phma.hn.org>:

> On Wednesday 03 November 2004 10:57, jordi mas wrote:
> > {coi xorxes}, by saying "a translation" like that
> > you are assuming that the term originated in
> > English. But mathematics is definitely not such a
> > field. Maybe it was the other way round,
> > and historically "manifold" is a
> > translation of the Romance "variété/variedad".
> 
> I've seen "linear variety" in English.
> 
> > > I propose {cmacyvrici}.
> >
> > Me too.
> 
> With what place structure? "x1 is a manifold/variety with properties x2"? Can 
> something be mathematically various?

Please note that "variety" has a couple of distinct mathematical meanings
itself - one in algebraic geometry and one in universal algebra.

I think ju'oru'e it's possible to link the algebraic geometric meaning to
manifolds, but I certainly don't think they should get the same lujvo or
fu'ivla. We can probably manage without words for these types of 'variety',
but be careful with your definitions!

However, pe'i {cmacyvrici} misses the point of manifolds, which is that they
are locally Euclidean. That the Euclidean spaces they locally resemble can
vary is perhaps secondary.

Maybe {diklykurfycanlu} aka {klokurca'u}.

If you have a better word for "Euclidean space" than {kurca'u}, substitute
that in.