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Group theory --- Operator theory --- 51 --- Mathematics --- Partially ordered spaces. --- Semigroups of operators. --- 51 Mathematics
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Partially ordered spaces --- Linear topological spaces, Ordered --- Linear topological spaces --- Vector spaces --- Generalized spaces
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Functional analysis --- Banach spaces. --- Partially ordered spaces. --- Riesz spaces. --- Locally convex spaces. --- Banach, Espaces de --- Espaces partiellement ordonnés --- Riesz, Espaces de --- Espaces localement convexes --- Banach spaces --- Partially ordered spaces --- Riesz spaces --- Locally convex spaces --- Espaces partiellement ordonnés --- Analyse fonctionnelle --- Espaces vectoriels topologiques ordonnés --- Linear topological spaces, Ordered --- Espaces vectoriels topologiques ordonnés. --- Functional analysis. --- Linear topological spaces, Ordered. --- Espaces vectoriels ordonnes
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In mathematical modeling of processes one often encounters optimization problems involving more than one objective function, so that Multiobjective Optimization (or Vector Optimization) has received new impetus. The growing interest in multiobjective problems, both from the theoretical point of view and as it concerns applications to real problems, asks for a general scheme which embraces several existing developments and stimulates new ones. In this book the authors provide the newest results and applications of this quickly growing field. This book will be of interest to graduate students in mathematics, economics, and engineering, as well as researchers in pure and applied mathematics, economics, engineering, geography, and town planning. A sound knowledge of linear algebra and introductory real analysis should provide readers with sufficient background for this book.
Mathematics. --- Operations research. --- Management science. --- Operations Research, Management Science. --- Vector spaces. --- Partially ordered spaces. --- Mathematical optimization. --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory
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This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces
Riesz spaces. --- Partially ordered spaces. --- Vector spaces. --- Linear spaces --- Linear vector spaces --- Algebras, Linear --- Functional analysis --- Vector analysis --- Spaces, Partially ordered --- Ordered topological spaces --- Topological spaces --- Riesz vector spaces --- Vector lattices --- Lattice theory --- Vector spaces
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Topological groups. Lie groups --- Differential geometry. Global analysis --- Complex manifolds --- Partially ordered spaces --- Semisimple Lie groups --- Flag manifolds --- 512 --- Flag varieties (Mathematics) --- Manifolds, Flag --- Varieties, Flag (Mathematics) --- Algebraic varieties --- Semi-simple Lie groups --- Lie groups --- Spaces, Partially ordered --- Ordered topological spaces --- Topological spaces --- Analytic spaces --- Manifolds (Mathematics) --- Algebra --- 512 Algebra --- Complex manifolds. --- Lie groups. --- Partially ordered spaces. --- Espaces partiellement ordonnés. --- Lie, Groupes de. --- Variétés complexes.
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