Topologies on closed and closed convex sets:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1993
|
| Series: | Mathematics and its applications
268 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XI, 340 S. graph. Darst. |
| ISBN: | 9789048143337 0792325311 |
Staff View
MARC
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| 100 | 1 | |a Beer, Gerald |e Verfasser |0 (DE-588)1156974135 |4 aut | |
| 245 | 1 | 0 | |a Topologies on closed and closed convex sets |c by Gerald Beer |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1993 | |
| 300 | |a XI, 340 S. |b graph. Darst. | ||
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| 490 | 1 | |a Mathematics and its applications |v 268 | |
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| 650 | 4 | |a Metric spaces | |
| 650 | 4 | |a Normed linear spaces | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Preface ix
Chapter 1. Preliminaries 1
Section 1.1 Notation and Background Material 1
Section 1.2 Weak Topologies 8
Section 1.3 Semicontinuous Functions 13
Section 1.4 Convex Sets and the Separation Theorem 20
Section 1.5 Gap and Excess 28
Chapter 2. Weak Topologies Determined by Distance Functionals 34
Section 2.1 The Wijsman Topology 34
Section 2.2 Hit and Miss Topologies and the Wijsman Topology 43
Section 2.3 UC Spaces 54
Section 2.4 The Slice Topology 60
Section 2.5 Complete Metrizability of the Wijsman and Slice Topologies 69
Chapter 3. The Attouch Wets and Hausdorff Metric Topologies 78
Section 3.1 The Attouch Wets Topology 78
Section 3.2 The Hausdorff Metric topology 85
Section 3.3 Varying the Metrics 92
Section 3.4 Set Convergence and Strong Convergence of Linear Functionals 100
Chapter 4. Cap and Excess Functionals and Weak Topologies 106
Section 4.1 Families of Gap and Excess Functionals 106
Section 4.2 Presentations of the Attouch Wets and Hausdorff Metric Topologies 113
Section 4.3 The Scalar Topology and the Linear Topology for Convex Sets 121
Section 4.4 Weak Topologies determined by Infimal Value Functionals 128
viii
Chapter 5. The Fell Topology and Kuratowski Painleve Convergence 138
Section 5.1 The Fell Topology 138
Section 5.2 Kuratowski Painlevd Convergence 145
Section 5.3 Epi convergencc 155
Section 5.4 Mosco Convergence and the Mosco Topology 170
Section 5.5 Mosco Convergence versus Wijsman Convergence 178
Chapter 6. Multifunctions : The Rudiments 183
Section 6.1 Multifunctions 184
Section 6.2 Lower and Upper Semicontinuity for Multifunctions 192
Section 6.3 Outer Semicontinuity versus Upper Semicontinuity 199
Section 6.4 KKM Maps and their Application 208
Section 6.5 Measurable Multifunctions 216
Section 6.6 Two Selection Theorems 228
Chapter 7. The Attouch Wets Topology for Convex Functions 235
Section 7.1 Attouch Wets Convergence of Epigraphs 235
Section 7.2 Continuity of Polarity and the Attouch Wets Topology 241
Section 7.3 Regularization of Convex Functions and Attouch Wets Convergence 250
Section 7.4 The Sum Theorem 256
Section 7.5 Convex Optimization and the Attouch Wets Topology 264
Chapter 8. The Slice Topology for Convex Functions 270
Section 8.1 Slice and Dual Slice Convergence of Convex Functions 270
Section 8.2 Convex Duality and the Slice Topology 276
Section 8.3 Subdifferentials of Convex Functions and the Slice Topology 287
Section 8.4 Stability of the Geometric Ekeland Principle 299
Notes and References 306
Bibliography 315
Symbols and Notation 331
Subject Index 335
|
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)28722704 (DE-599)BVBBV008833127 |
| dewey-full | 514/.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.32 |
| dewey-search | 514/.32 |
| dewey-sort | 3514 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV008833127 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:25:44Z |
| institution | BVB |
| isbn | 9789048143337 0792325311 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005839953 |
| oclc_num | 28722704 |
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| owner | DE-12 DE-824 DE-384 DE-11 DE-739 |
| owner_facet | DE-12 DE-824 DE-384 DE-11 DE-739 |
| physical | XI, 340 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Beer, Gerald Verfasser (DE-588)1156974135 aut Topologies on closed and closed convex sets by Gerald Beer Dordrecht u.a. Kluwer Acad. Publ. 1993 XI, 340 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 268 Hier auch später erschienene, unveränderte Nachdrucke Hyperspace Metric spaces Normed linear spaces Topology Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Geordneter topologischer Vektorraum (DE-588)4156755-9 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Hyperraum (DE-588)4161087-8 gnd rswk-swf Geordneter topologischer Vektorraum (DE-588)4156755-9 s DE-604 Metrischer Raum (DE-588)4169745-5 s Topologie (DE-588)4060425-1 s Hyperraum (DE-588)4161087-8 s Mathematics and its applications 268 (DE-604)BV008163334 268 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005839953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beer, Gerald Topologies on closed and closed convex sets Mathematics and its applications Hyperspace Metric spaces Normed linear spaces Topology Metrischer Raum (DE-588)4169745-5 gnd Geordneter topologischer Vektorraum (DE-588)4156755-9 gnd Topologie (DE-588)4060425-1 gnd Hyperraum (DE-588)4161087-8 gnd |
| subject_GND | (DE-588)4169745-5 (DE-588)4156755-9 (DE-588)4060425-1 (DE-588)4161087-8 |
| title | Topologies on closed and closed convex sets |
| title_auth | Topologies on closed and closed convex sets |
| title_exact_search | Topologies on closed and closed convex sets |
| title_full | Topologies on closed and closed convex sets by Gerald Beer |
| title_fullStr | Topologies on closed and closed convex sets by Gerald Beer |
| title_full_unstemmed | Topologies on closed and closed convex sets by Gerald Beer |
| title_short | Topologies on closed and closed convex sets |
| title_sort | topologies on closed and closed convex sets |
| topic | Hyperspace Metric spaces Normed linear spaces Topology Metrischer Raum (DE-588)4169745-5 gnd Geordneter topologischer Vektorraum (DE-588)4156755-9 gnd Topologie (DE-588)4060425-1 gnd Hyperraum (DE-588)4161087-8 gnd |
| topic_facet | Hyperspace Metric spaces Normed linear spaces Topology Metrischer Raum Geordneter topologischer Vektorraum Topologie Hyperraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005839953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT beergerald topologiesonclosedandclosedconvexsets |