Domain-valued maxitive maps and their representations

Details Domain-valued maxitive maps and their representations Domain-valued maxitive maps and their representations

2010-01-03

arxiv.org/abs/1001.0158v1

Mathematics

General Topology

17 pages

Scientific paper

The recent extensions of domain theory have proved particularly efficient to study lattice-valued maxitive measures, when the target lattice is continuous. Maxitive measures are defined analogously to classical measures with the supremum operation in place of the addition. Building further on the links between domain theory and idempotent analysis highlighted by Lawson (2004), we introduce the concept of domain-valued maxitive maps, which we define as a ``point-free'' version of maxitive measures. In addition to investigating representations of maxitive maps, we address some extension problems. Our analysis is carried out in the general Z framework of domain theory.

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