Subject: manuscript on domain theory available
From: Michael Bukatin (bukatin@cs.brandeis.edu)
Date: Mon Mar 26 2001 - 14:35:37 EST
(apologies, if you received multiple copies of this)
The manuscript of my dissertation "Mathematics of Domains"
(245K, 136 pages) is now available at
http://www.cs.brandeis.edu/~bukatin/thesis.ps.gz
Comments, feedback, and critique are welcome.
Among the topics of possible interest:
Chapter 5. Reformulation of algebraic information systems
allowing to define effective information systems in a more
general way (via recursively enumerable sets, rather than
via recursive sets).
Chapter 6. Explanation of non-reflexive logic of
continuous information systems (Hoofman). Generalization
of this logic beyond the continuous case.
Chapter 7. Theory of algebraic subdomains.
Chapter 8. Simple criteria of finitarity for retractions
and projections.
Chapter 9. Theory of co-continuous valuations.
Chapter 10. Theory of relaxed metrics. Scheme of computation
of Scott continuous effective relaxed metrics via
recursive enumeration.
Chapter 11. Construction of Scott continuous relaxed metrics
from co-continuous valuations.
Chapter 12. Theory of negative information for domains,
which are not non-weakly Hausdorff (Escardo).
The relationships of this theory with the condition
of equality of relative Scott and Lawson topologies on
the subspace of maximal elements (Lawson), and with
topological tolerance spaces (Smyth).
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