Elementary topical functions on \(b\)-complete semimodules over \(b\)-complete idempotent semifields

DOI10.1016/j.laa.2010.07.019zbMath1211.06010OpenAlexW1984644662MaRDI QIDQ603143

Ivan Singer

Publication date: 5 November 2010

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.07.019

zbMATH Keywords

semimoduleidempotent semifieldorder topologytopical function\(b\)-completedownward set

Mathematics Subject Classification ID

Ordered topological structures (06F30) Ordered rings, algebras, modules (06F25)

Related Items (4)

Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions ⋮ Extended-valued topical and anti-topical functions on semimodules. ⋮ Characterizations of minimal elements of topical functions on semimodules with applications ⋮ Topical functions on semimodules and generalizations

Cites Work

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• Duality and separation theorems in idempotent semimodules.
• Linear functionals on idempotent spaces. An algebraic approach
• Downward sets and their separation and approximation properties
• Best approximation by downward sets with applications
• Topologies on lattice ordered groups, separation from closed downward sets and conjugations of type Lau
• Topical and sub-topical functions, downward sets and abstract convexity
• The Perron-Frobenius theorem for homogeneous, monotone functions
• Abstract convexity:examples and applications
• Best approximation by normal and conormal sets
• Idempotent functional analysis: An algebraic approach

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