Topological cones: functional analysis in a \(T_{0}\)-setting

DOI10.1007/s00233-008-9078-0zbMath1151.22006OpenAlexW2056100909MaRDI QIDQ938295

Klaus Keimel

Publication date: 19 August 2008

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00233-008-9078-0

zbMATH Keywords

coneHahn-Banach-type theoremspowerdomains in semanticsprobability and nondeterminismtopological cone

Mathematics Subject Classification ID

Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Semantics in the theory of computing (68Q55) Continuous lattices and posets, applications (06B35) Topological and differentiable algebraic systems (22A99)

Related Items (16)

Algebras of the extended probabilistic powerdomain monad ⋮ In memoriam: Klaus Keimel (1939--2017) ⋮ Completing simple valuations in K-categories ⋮ Probability, valuations, hyperspace: Three monads on top and the support as a morphism ⋮ О вложении однозначно делимой абелевой полугруппы в выпуклый конус ⋮ A construction of free dcpo-cones ⋮ Extending algebraic operations to D-completions ⋮ Isomorphism theorems between models of mixed choice ⋮ The Cuntz semigroup and domain theory ⋮ Abstract ordered compact convex sets and algebras of the (sub)probabilistic powerdomain monad over ordered compact spaces ⋮ Fixed points and completeness in metric and generalized metric spaces ⋮ HAHN-BANACH TYPE THEOREMS ON FUNCTIONAL SEPARATION FOR CONVEX ORDERED NORMED CONES ⋮ Kantorovich-Rubinstein quasi-metrics IV: lenses, quasi-lenses and forks ⋮ Kantorovich-Rubinstein quasi-metrics. III: Spaces of sublinear and superlinear previsions ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• The probabilistic powerdomain for stably compact spaces
• Order and convexity in potential theory: H-cones. In collab. with Herbert Höllein
• Ordered cones and approximation
• The bounded-complete hull of an \(\alpha\)-space
• Lokal kompakte Kegelhalbgruppen und deren Einbettung in topologische Vektorräume
• Continuous Lattices and Domains
• A domain-theoretic Banach–Alaoglu theorem
• Some results on Hahn--Banach-type theorems for continuous D-cones
• Partial correctness for probabilistic demonic programs
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