Many valued topology and its applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston, Mass. [u.a.]
Kluwer Acad. Publ.
2001
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 382 Seiten graph. Darst. |
| ISBN: | 0792373189 |
Internformat
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| 245 | 1 | 0 | |a Many valued topology and its applications |c Ulrich Höhle |
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Datensatz im Suchindex
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| adam_text | MANY VALUED TOPOLOGY AND ITS APPLICATIONS ULRICH HOHLE FACHBEREICH
MATHEMATIK BERGISCHE UNIVERSITDT, WUPPERTAL, GERMANY KLUWER ACADEMIC
PUBLISHERS BOSTON/DORDRECHT/LONDON CONTENTS INTRODUCTION CATEGORICAL
FOUNDATIONS 11 CATEGORICAL PRELIMINARIES 13 1.1 (EPI, EXTREMAL
MONO)-CATEGORIES 13 1.2 MONADS 16 1.3 PROBLEMS 25 PARTIALLY ORDERED
MONADS 29 2.1 PARTIALLY ORDERED OBJECTS 29 2.2 TRACE OF PARTIALLY
ORDERED OBJECTS 38 2.3 AXIOMS OF PARTIALLY ORDERED MONADS IN C 42 2.4
SOME EXAMPLES OF ORDERED MONADS 48 2.4.1 Q-VALUED PROPER POWER SET MONAD
IN SET 49 2.4.2 (3-VALUED FILTER MONAD IN SET 50 2.5 PROBLEMS 53
CATEGORICAL BASIS OF TOPOLOGY 55 3.1 TOPOLOGICAL SPACE OBJECTS 55 3.2
DENSITY AND CLOSED HULLS 60 3.3 THE HAUSDORFF SEPARATION AXIOM 67 3.4
THE REGULARITY AXIOM 72 3.5 COMPACTNESS 89 3.6 PROBLEMS 103 II MANY
VALUED TOPOLOGY 105 4 QUANTIC BASIS OF FILTER THEORY 107 4.1 GL-MONOIDS
WITH SQUARE ROOTS 109 4.2 Q-VALUED FILTERS 120 4.3 STRATIFIED *-VALUED
FILTERS 125 4.4 EXAMPLES OF STRATIFIED 0*-VALUED FILTERS 137 CONTENTS
4.5 PROBLEMS 143 MANY VALUED TOPOLOGICAL SPACES 145 5.1 MOTIVATING
PROBLEM 146 5.2 AXIOMS OF MANY VALUED TOPOLOGIES 149 5.3 MANY VALUED
SPATIALITY AND SOBRIFICATIONS 158 5.3.1 -SOBRIFICATION AND SPECTRAL
THEORY IN HILBERT SPACES ... 159 5.3.2 B(FI)-SOBRIFICATION AND ALMOST
EVERYWHERE DEFINED RANDOM VARIABLES 165 5.3.3 BOOLEAN VALUED TOPOLOGIES
AND FRAMES 171 5.4 0-VALUED TOPOLOGIES AND CONVERGENCE 174 5.4.1 HEYTING
ALGEBRA VALUED TOPOLOGIES AND LIMIT STRUCTURES . . 176 5.5 STRATIFIED
C-VALUED TOPOLOGICAL SPACES 180 5.5.1 RIGID, MANY VALUED REAL LINE 188
5.6 CHANGE OF BASIS 194 5.6.1 SPATIAL FRAMES AND THE HYPERGRAPH FUNCTOR
200 5.7 PROBLEMS 202 MANY VALUED CONVERGENCE THEORY 205 6.1 DENSITY AND
CLOSED SUBSETS 208 6.2 LIMIT POINTS AND THE MANY VALUED T 2 -AXIOM 212
6.2.1 T2-AXIOM AND QUANTALE VALUED TOPOLOGIES 215 6.2.2 THE TJ-AXIOM AND
STRATIFIED 9*-VALUED TOPOLOGIES . . . . 217 6.3 THE MANY VALUED
REGULARITY AXIOM 220 6.3.1 REGULAR HEYTING ALGEBRA VALUED TOPOLOGICAL
SPACES .... 222 6.3.2 STAR-REGULAR, RIGID .-VALUED TOPOLOGICAL SPACES
226 6.4 MANY VALUED COMPACTNESS 235 6.4.1 COMPACT, HEYTING ALGEBRA
VALUED TOPOLOGICAL SPACES . . . 236 6.4.2 STAR-COMPACTNESS AND THE
STRATIFICATION AXIOM 243 6.5 PROBLEMS 249 III APPLICATIONS OF MANY
VALUED TOPOLOGY 253 7 STOCHASTIC METRICS 255 7.1 STOCHASTIC METRIC
SPACES 255 7.2 TOPOLOGICAL PROPERTIES OF STOCHASTIC METRICS 259 7.3
PROBLEMS 277 8 STOCHASTIC PROCESSES 279 8.1 OUTER MEASURES AND
STOCHASTIC PROCESSES 279 8.2 LINEAR STOCHASTIC PROCESSES 283 8.3
UNIFORMLY CONTINUOUS TRAJECTORIES 287 8.4 CONTINUOUS LINEAR TRAJECTORIES
290 8.4.1 MINLOS THEOREM 299 8.5 PROBLEMS 314 CONTENTS 3 9 PROBABILITY
MEASURES 317 9.1 &R M -VALUED COMPACTIFICATIONS 317 9.2 &T M -VALUED
CONTINUOUS EXTENSIONS 325 9.3 PROBLEMS 329 10 TOPOLOGIES ON M-VALUED
SETS 331 10.1 LOCAL M-VALUED FILTER MONAD 335 10.2 TOPOLOGICAL AXIOMS
FOR M-VALUED SETS 350 10.2.1 TOPOLOGIES ON M-VALUED SETS AS SHEAVES OVER
M 356 10.3 PROBLEMS 359 APPENDIX 361 A.I REGULARITY BASED ON
ORTHOLATTICES 361 A.2 TOPOLOGIZATION OF MENGER SPACES 364 BIBLIOGRAPHY
367 AUTHOR INDEX 375 SUBJECT INDEX 377
|
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| callnumber-first | Q - Science |
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| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013960146 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:55:08Z |
| institution | BVB |
| isbn | 0792373189 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009553619 |
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| physical | 382 Seiten graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
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| publisher | Kluwer Acad. Publ. |
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| spelling | Höhle, Ulrich 1943- Verfasser (DE-588)1013286766 aut Many valued topology and its applications Ulrich Höhle Boston, Mass. [u.a.] Kluwer Acad. Publ. 2001 382 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Topology Monade Mathematik (DE-588)4512463-2 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Topologie (DE-588)4060425-1 s Monade Mathematik (DE-588)4512463-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009553619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Höhle, Ulrich 1943- Many valued topology and its applications Topology Monade Mathematik (DE-588)4512463-2 gnd Topologie (DE-588)4060425-1 gnd |
| subject_GND | (DE-588)4512463-2 (DE-588)4060425-1 |
| title | Many valued topology and its applications |
| title_auth | Many valued topology and its applications |
| title_exact_search | Many valued topology and its applications |
| title_full | Many valued topology and its applications Ulrich Höhle |
| title_fullStr | Many valued topology and its applications Ulrich Höhle |
| title_full_unstemmed | Many valued topology and its applications Ulrich Höhle |
| title_short | Many valued topology and its applications |
| title_sort | many valued topology and its applications |
| topic | Topology Monade Mathematik (DE-588)4512463-2 gnd Topologie (DE-588)4060425-1 gnd |
| topic_facet | Topology Monade Mathematik Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009553619&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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