Topologies on Closed and Closed Convex SetsSpringer Science & Business Media, 1993 M10 31 - 340 páginas This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text. This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics. |
Contenido
II | 1 |
IV | 8 |
V | 13 |
VI | 20 |
VII | 28 |
VIII | 34 |
IX | 43 |
X | 54 |
XXIX | 178 |
XXX | 183 |
XXXI | 184 |
XXXII | 192 |
XXXIII | 199 |
XXXIV | 208 |
XXXV | 216 |
XXXVI | 228 |
XI | 60 |
XII | 69 |
XIII | 78 |
XV | 85 |
XVI | 92 |
XVII | 100 |
XVIII | 106 |
XX | 113 |
XXI | 121 |
XXII | 128 |
XXIII | 138 |
XXVI | 145 |
XXVII | 155 |
XXVIII | 170 |
XXXVII | 235 |
XXXVIII | 241 |
XXXIX | 250 |
XL | 256 |
XLI | 264 |
XLII | 270 |
XLIV | 276 |
XLV | 287 |
XLVI | 299 |
XLVII | 306 |
XLVIII | 315 |
XLIX | 331 |
335 | |
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Términos y frases comunes
Argmin Attouch-Wets convergence Attouch-Wets topology Banach space bounded subsets choose closed convex subsets closed sets compact subset continuous functions convex functions convex sets convex subsets distance functionals dual epi fn epif epigraphs exists Fell topology finite fixed function f graph Hausdorff metric Hausdorff metric topology Hausdorff space hyperspace topologies K-lim Kuratowski-Painlevé convergence Lemma Let X,d Let X,II Let X,II-II lower semicontinuous lower semicontinuous functions Math measurable metric space X,d Mosco convergence multifunction neighborhood nonempty closed subsets normed linear space open subset pointwise convergence Proof proper lower semicontinuous Proposition Prove proximal topology resp result scalar sequence Show sigma algebra slice convergence slice topology slv f space and let subbase Suppose T(xo TAW-lim Theorem topology on CL(X uniform convergence upper semicontinuity Vietoris topology weak topology weak topology determined weakly compact Wijsman convergence Wijsman topology
Pasajes populares
Página 328 - On the convergence of sequences of convex sets in finite dimensions.
Página 328 - In: Selected Topics in Operations Research and Mathematical Economics (G. Hammer and D. Pallaschke, eds.), Lecture Notes Econ. Math. Systems 226, Springer- Verlag, Berlin, Heidelberg, 1984, 49-79. [237] I. Singer, Conjugation operators. In: Selected Topics in Operations Research and Mathematical Economics (G.