Formal Topology and Domains
Giovanni Sambin · Electronic Notes in Theoretical Computer Science · 2000
The theme of this paper is the relation between formal topology and the theory of domains. On one hand, domain theory can be seen as a branch of formal topology. On the other hand, the influence of domain theory on formal topology is twofold. Historically, the presence of the subset Con in Scott's information systems has been the starting point for the introduction of the positivity predicate Pos in formal topology; also, the notion of approximable mapping has influenced the definition of continuous relations between formal topologies. Conceptually, since domain theory can be seen as a particular case, any notion and result in domain theory becomes a challenge for formal topology: how much of domain theory can be generalized to formal topology? My impression is that some open problems in one of the two fields could already have a solution in the other, and that is why an intensification of contact should be rewarding.1