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Logic of Fixed Points and Scott Topology
by
Michael Bukatin
Brandeis University
Spaces with Scott topologies are frequently defined as sets of fixed points of retractions or, more generally, arbitrary Scott continuous transformations. For the case of retractions, the logical approach to this technique was developed by Hoofman under the name of Continuous Information Systems. We present this approach for general Scott continuous transformations, together with its underlying intuition, a number of applications to closure operations and finitary retractions, and a spectrum of outstanding open problems. The details are available in my manuscript "Mathematics of Domains" (Chapters 5-8), http://www.cs.brandeis.edu/ ~ bukatin/thesis.ps.gz.
Date received: May 14, 2001
Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-36.