Boolean Algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1960
|
| Edition: | Second Edition |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge
25 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the development of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2] and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No knowledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs |
| Physical Description: | 1 Online-Ressource (X, 237 p) |
| ISBN: | 9783662015070 9783662015094 |
| DOI: | 10.1007/978-3-662-01507-0 |
Staff View
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV042423188 |
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| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783662015070 9783662015094 |
| language | English |
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| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1960 |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge |
| spelling | Sikorski, Roman 1920-1983 Verfasser (DE-588)1035622769 aut Boolean Algebras by Roman Sikorski Second Edition Berlin, Heidelberg Springer Berlin Heidelberg 1960 1 Online-Ressource (X, 237 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge 25 There are two aspects to the theory of Boolean algebras; the algebraic and the set-theoretical. A Boolean algebra can be considered as a special kind of algebraic ring, or as a generalization of the set-theoretical notion of a field of sets. Fundamental theorems in both of these directions are due to M. H. STONE, whose papers have opened a new era in the development of this theory. This work treats the set-theoretical aspect, with little mention being made of the algebraic one. The book is composed of two chapters and an appendix. Chapter I is devoted to the study of Boolean algebras from the point of view of finite Boolean operations only; a greater part of its contents can be found in the books of BIRKHOFF [2] and HERMES [1]. Chapter II seems to be the first systematic study of Boolean algebras with infinite Boolean operations. To understand Chapters I and II it suffices only to know fundamental notions from general set theory and set-theoretical topology. No knowledge of lattice theory or of abstract algebra is presumed. Less familiar topological theorems are recalled, and only a few examples use more advanced topological means; but these may be omitted. All theorems in both chapters are given with full proofs Mathematics Computer science Real Functions Mathematics, general Mathematical Logic and Formal Languages Informatik Mathematik 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 1\p DE-604 Boolescher Verband (DE-588)4146289-0 s 2\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" Neue Folge 25 (DE-604)BV005871160 25 https://doi.org/10.1007/978-3-662-01507-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sikorski, Roman 1920-1983 Boolean Algebras Mathematics Computer science Real Functions Mathematics, general Mathematical Logic and Formal Languages Informatik Mathematik 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 by Roman Sikorski |
| title_fullStr | Boolean Algebras by Roman Sikorski |
| title_full_unstemmed | Boolean Algebras by Roman Sikorski |
| title_short | Boolean Algebras |
| title_sort | boolean algebras |
| topic | Mathematics Computer science Real Functions Mathematics, general Mathematical Logic and Formal Languages Informatik Mathematik Boolesche Algebra (DE-588)4146280-4 gnd Boolescher Verband (DE-588)4146289-0 gnd |
| topic_facet | Mathematics Computer science Real Functions Mathematics, general Mathematical Logic and Formal Languages Informatik Mathematik Boolesche Algebra Boolescher Verband |
| url | https://doi.org/10.1007/978-3-662-01507-0 |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT sikorskiroman booleanalgebras |