Partializing Stone Spaces using SFP domains
by
Paolo Baldan
Dipartimento di Matematica e Informatica, Universitá di Udine, via delle Scienze 208, 33100, Udine (Italy)
Coauthors: Fabio Alessi, Furio Honsell

The problem of finding an appropriate "partialization" of a space of total elements, arises in several areas of Mathematics and Computer Science when dealing with computational approximations. In this paper we investigate the problem of "partializing" Stone spaces by "Sequence of Finite Posets" (SFP) domains. More specifically, we introduce a suitable subcategory SFP^m of SFP which is naturally related to the category of 2nd countable Stone spaces 2-Stone by the functor MAX, which associates to each object of SFP^m the space of its maximal elements endowed with the induced Scott topology. The category SFP^m is closed under limits as well as many domain constructors, such as lifting, sum, product and Plotkin powerdomain. The functor MAX preserves limits and commutes with these constructors. Thus, SFP domains which "partialize" solutions of a vast class of domain equations in 2-Stone, can be obtained by solving the corresponding equations in SFP^m. Furthermore, we compare two classical partializations of the space of Milner's Synchronization Trees using SFP domains introduced by Abramsky and Mislove, Moss and Oles. Using the notion of "rigid" embedding projection pair, we show that the two domains are not isomorphic, thus providing a negative answer to an open problem raised by Mislove, Moss and Oles.

Date received: July 3, 1997

Copyright © 1997 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 # caao-81.