Boolean Algebras:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1960
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge
25 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-662-01507-0 |
| Beschreibung: | 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 |
| Umfang: | 1 Online-Ressource (X, 237 p) |
| ISBN: | 9783662015070 9783662015094 |
| DOI: | 10.1007/978-3-662-01507-0 |
Internformat
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042423188 | ||
| 003 | DE-604 | ||
| 005 | 20171009 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1960 xx o|||| 00||| eng d | ||
| 020 | |a 9783662015070 |c Online |9 978-3-662-01507-0 | ||
| 020 | |a 9783662015094 |c Print |9 978-3-662-01509-4 | ||
| 024 | 7 | |a 10.1007/978-3-662-01507-0 |2 doi | |
| 035 | |a (OCoLC)1184500415 | ||
| 035 | |a (DE-599)BVBBV042423188 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.8 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Sikorski, Roman |d 1920-1983 |e Verfasser |0 (DE-588)1035622769 |4 aut | |
| 245 | 1 | 0 | |a Boolean Algebras |c by Roman Sikorski |
| 250 | |a Second Edition | ||
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1960 | |
| 300 | |a 1 Online-Ressource (X, 237 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge |v 25 | |
| 500 | |a 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 | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Computer science | |
| 650 | 4 | |a Real Functions | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematical Logic and Formal Languages | |
| 650 | 4 | |a Informatik | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Boolesche Algebra |0 (DE-588)4146280-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Boolescher Verband |0 (DE-588)4146289-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Boolesche Algebra |0 (DE-588)4146280-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Boolescher Verband |0 (DE-588)4146289-0 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 810 | 2 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" |t Neue Folge |v 25 |w (DE-604)BV005871160 |9 25 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-662-01507-0 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027858605 | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 2070197 |
|---|---|
| _version_ | 1821931358843305984 |
| any_adam_object | |
| author | Sikorski, Roman 1920-1983 |
| author_GND | (DE-588)1035622769 |
| author_facet | Sikorski, Roman 1920-1983 |
| author_role | aut |
| author_sort | Sikorski, Roman 1920-1983 |
| author_variant | r s rs |
| building | Verbundindex |
| bvnumber | BV042423188 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184500415 (DE-599)BVBBV042423188 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-01507-0 |
| edition | Second Edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03449nam a2200577zcb4500</leader><controlfield tag="001">BV042423188</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20171009 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1960 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662015070</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-662-01507-0</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783662015094</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-662-01509-4</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-662-01507-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1184500415</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042423188</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.8</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Sikorski, Roman</subfield><subfield code="d">1920-1983</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1035622769</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Boolean Algebras</subfield><subfield code="c">by Roman Sikorski</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second Edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1960</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 237 p)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge</subfield><subfield code="v">25</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer science</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Real Functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, general</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical Logic and Formal Languages</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Informatik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Boolesche Algebra</subfield><subfield code="0">(DE-588)4146280-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Boolescher Verband</subfield><subfield code="0">(DE-588)4146289-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Boolesche Algebra</subfield><subfield code="0">(DE-588)4146280-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Boolescher Verband</subfield><subfield code="0">(DE-588)4146289-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" </subfield><subfield code="t">Neue Folge</subfield><subfield code="v">25</subfield><subfield code="w">(DE-604)BV005871160</subfield><subfield code="9">25</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-662-01507-0</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858605</subfield></datafield></record></collection> |
| id | DE-604.BV042423188 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:48Z |
| institution | BVB |
| isbn | 9783662015070 9783662015094 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858605 |
| oclc_num | 1184500415 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 237 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1960 |
| publishDateSearch | 1960 |
| publishDateSort | 1960 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, Unter Mitwirkung der Schriftleitung des "Zentralblatt für Mathematik" : Neue Folge |
| 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 |