Boolean algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1969
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 237 S. |
Internformat
MARC
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| 100 | 1 | |a Sikorski, Roman |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Boolean algebras |c Roman Sikorski |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin u.a. |b Springer |c 1969 | |
| 300 | |a X, 237 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge |v 25 | |
| 650 | 4 | |a Boole, Algèbre de | |
| 650 | 4 | |a Algebra, Boolean | |
| 650 | 0 | 7 | |a Boolesche Algebra |0 (DE-588)4146280-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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| adam_text | Contents
Terminology and notation 1
Chapter I. Finite joins and meets
§ 1. Definition of Boolean algebras 3
§ 2. Some consequences of the axioms 6
§ 3. Ideals and filters 11
§ 4. Subalgebras 13
§ 5. Homomorphisms, isomorphisms 15
§ 6. Maximal ideals and filters 17
§ 7. Reduced and perfect fields of sets 20
§ 8. A fundamental representation theorem 23
§ 9. Atoms 27
§ 10. Quotient algebras 29
§11. Induced homomorphisms between fields of sets 32
§ 12. Theorems on extending to homomorphisms 35
§ 13. Independent subalgebras. Products 39
§ 14. Free Boolean algebras 42
§ 15. Induced homomorphisms between quotient algebras 45
§ 16. Direct unions 50
§ 17. Connection with algebraic rings 51
Chapter II. Infinite joins and meets
§ 18. Definition 54
§ 19. Algebraic properties of infinite joins and meets, (m, tl) distributivity . 59
§ 20. m complete Boolean algebras 65
§21. m ideals and m filters. Quotient algebras 74
§ 22. m homomorphisms. The interpretation in Stone spaces 81
§ 23. m subalgebras 91
§ 24. Representations by m fields of sets 97
§ 25. Complete Boolean algebras 105
§26. The field of all subsets of a set 110
§27. The field of all Borel subsets of a metric space 114
§28. Representation of quotient algebras as fields of sets 115
§ 29. A fundamental representation theorem for Boolean j algebras.
m representability 117
§ 30. Weak tn distributivity 127
§31. Free Boolean tn algebras 131
§ 32. Homomorphisms induced by point mappings 136
§ 33, Theorems on extension of homomorphisms 141
§ 34. Theorems on extending to homomorphisms 144
§ 35. Completions and m completkms 152
§ 36. Extensions of Boolean algebras 165
§ 37. m independent subalgebras. The field tn product 172
§ 38. Boolean (ttl, n) products 175
X Contents
Appendix
§ 39. Relation to other algebras 191
§ 40. Applications to mathematical logic. Classical calculi 194
§ 41. Topology in Boolean algebras. Applications to non classical logic . . 198
§ 42. Applications to measure theory 201
§ 43. Measurable functions and real homomorphisms 204
§ 44. Measurable functions. Reduction to continuous functions 206
§ 45. Applications to functional analysis 207
§ 46. Applications to foundations of the theory of probability 208
§ 47. Problems of effectivity 210
Bibliography 212
List of symbols 231
Author Index 232
Subject Index 235
|
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| classification_rvk | SK 150 |
| ctrlnum | (OCoLC)11243 (DE-599)BVBBV001934074 |
| dewey-full | 512/.89 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.89 |
| dewey-search | 512/.89 |
| dewey-sort | 3512 289 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T15:37:29Z |
| institution | BVB |
| language | English |
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| physical | X, 237 S. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Springer |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge |
| spelling | Sikorski, Roman Verfasser aut Boolean algebras Roman Sikorski 3. ed. Berlin u.a. Springer 1969 X, 237 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge 25 Boole, Algèbre de Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd rswk-swf Boolescher Verband (DE-588)4146289-0 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 s DE-604 Boolescher Verband (DE-588)4146289-0 s Neue Folge Ergebnisse der Mathematik und ihrer Grenzgebiete 25 (DE-604)BV005871160 25 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sikorski, Roman Boolean algebras Boole, Algèbre de Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd Boolescher Verband (DE-588)4146289-0 gnd |
| subject_GND | (DE-588)4146280-4 (DE-588)4146289-0 |
| title | Boolean algebras |
| title_auth | Boolean algebras |
| title_exact_search | Boolean algebras |
| title_full | Boolean algebras Roman Sikorski |
| title_fullStr | Boolean algebras Roman Sikorski |
| title_full_unstemmed | Boolean algebras Roman Sikorski |
| title_short | Boolean algebras |
| title_sort | boolean algebras |
| topic | Boole, Algèbre de Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd Boolescher Verband (DE-588)4146289-0 gnd |
| topic_facet | Boole, Algèbre de Algebra, Boolean Boolesche Algebra Boolescher Verband |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT sikorskiroman booleanalgebras |