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BL
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| Record Number
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881349
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| Main Entry
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Beer, Gerald Alan.
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| Title & Author
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Topologies on closed and closed convex sets /\ by Gerald Beer.
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| Publication Statement
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Dordrecht ;Boston :: Kluwer Academic Publishers,, ©1993.
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| Series Statement
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Mathematics and its applications ;; v. 268
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| Page. NO
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xi, 340 pages :: illustrations ;; 25 cm.
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| ISBN
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0792325311
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: 9780792325314
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| Bibliographies/Indexes
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Includes bibliographical references (pages 315-330) and index.
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| Contents
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Ch. 1. Preliminaries. Sect. 1.1. Notation and Background Material. Sect. 1.2. Weak Topologies. Sect. 1.3. Semicontinuous Functions. Sect. 1.4. Convex Sets and the Separation Theorem. Sect. 1.5. Gap and Excess -- Ch. 2. Weak Topologies Determined by Distance Functionals. Sect. 2.1. The Wijsman Topology. Sect. 2.2. Hit-and-Miss Topologies and the Wijsman Topology. Sect. 2.3. UC Spaces. Sect. 2.4. The Slice Topology. Sect. 2.5. Complete Metrizability of the Wijsman and Slice Topologies -- Ch. 3. The Attouch-Wets and Hausdorff Metric Topologies. Sect. 3.1. The Attouch-Wets Topology. Sect. 3.2. The Hausdorff Metric topology. Sect. 3.3. Varying the Metrics. Sect. 3.4. Set Convergence and Strong Convergence of Linear Functionals -- Ch. 4. Gap and Excess Functionals and Weak Topologies. Sect. 4.1. Families of Gap and Excess Functionals. Sect. 4.2. Presentations of the Attouch-Wets and Hausdorff Metric Topologies. Sect. 4.3. The Scalar Topology and the Linear Topology for Convex Sets.
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Ch. 8. The Slice Topology for Convex Functions. Sect. 8.1. Slice and Dual Slice Convergence of Convex Functions. Sect. 8.2. Convex Duality and the Slice Topology. Sect. 8.3. Subdifferentials of Convex Functions and the Slice Topology. Sect. 8.4. Stability of the Geometric Ekeland Principle.
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Sect. 4.4. Weak Topologies determined by Infimal Value Functionals -- Ch. 5. The Fell Topology and Kuratowski-Painleve Convergence. Sect. 5.1. The Fell Topology. Sect. 5.2. Kuratowski-Painleve Convergence. Sect. 5.3. Epi-convergence. Sect. 5.4. Mosco Convergence and the Mosco Topology. Sect. 5.5. Mosco Convergence versus Wijsman Convergence -- Ch. 6. Multifunctions: The Rudiments. Sect. 6.1. Multifunctions. Sect. 6.2. Lower and Upper Semicontinuity for Multifunctions. Sect. 6.3. Outer Semicontinuity versus Upper Semicontinuity. Sect. 6.4. KKM Maps and their Application. Sect. 6.5. Measurable Multifunctions. Sect. 6.6. Two Selection Theorems -- Ch. 7. The Attouch-Wets Topology for Convex Functions. Sect. 7.1. Attouch-Wets Convergence of Epigraphs. Sect. 7.2. Continuity of Polarity and the Attouch-Wets Topology. Sect. 7.3. Regularization of Convex Functions and Attouch-Wets Convergence. Sect. 7.4. The Sum Theorem. Sect. 7.5. Convex Optimization and the Attouch-Wets Topology.
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| Subject
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Hyperspace.
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Metric spaces.
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Normed linear spaces.
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Topology.
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Espaces linéaires normés.
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Espaces métriques.
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Geordneter topologischer Vektorraum
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Hyperespace.
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Hyperraum
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Hyperspace.
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Metric spaces.
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Metrischer Raum
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Normed linear spaces.
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| Subject
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Topologie
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Topologie.
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Topology.
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hiperterek-- topológia (matematika)
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| Subject
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konvex geometria
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| Dewey Classification
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514/.32
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| LC Classification
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QA611.B38 1993
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| NLM classification
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msc54B20
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*54B20msc
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31.46bcl
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31.60bcl
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31.69bcl
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46B10msc
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46B20msc
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52-02msc
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52A07msc
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54-02msc
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54C60msc
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54C65msc
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54E05msc
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54E15msc
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54E35msc
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SK 150rvk
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SK 280rvk
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