Domain theory and hausdorff topologies
- From: John F <john@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 22 Jun 2007 01:37:02 +0000 (UTC)
How does the Lawson topology (which is T2/Hausdorff) differ
from Scott topology (T0/not Hausdorff) in the class of objects
that can be modelled by domains equipped with one topology
versus the other? Could you give me some example(s) of a
language/datatyoe/whatever that can be modelled using the Lawson
topology but not Scott (and/or vice versa)?
I'm also a little (maybe a lot) confused by the following
conundrum. Unless a topology is Hausdorff, a convergent
sequence doesn't necessarily converge to a unique limit.
So a convergent sequence (ordered set) of elements in a
Scott domain doesn't necessarily have a unique limit.
But, in the usual way, the lub of the (unordered set of)
compact elements way below any given element is always uniquely
that element. So the lub and limit operations seem to differ
in some essential way. How, exactly, does that work?
Thanks a lot.
--
John Forkosh ( mailto: j@xxxxx where j=john and f=forkosh )
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