Idempotent analysis and continuous semilattices (Q1434351)

The author gives an overview of various aspects of the recently emerging field of idempotent analysis and suggests potential connections with domain theory. The initial parts of the paper deal with idempotent semirings, semimodules, domain theory connections and max-plus algebras. Further, the author considers a discrete optimization problem that can be studied from the viewpoint of max-plus algebra and he uses a discrete-time Bellman equation. The concluding parts of the paper are devoted to function spaces, measures in idempotent analysis, deformations, asymptotics and superposition.