Lectures on Boolean Algebras
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1974
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042420490 | ||
| 003 | DE-604 | ||
| 005 | 20211012 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1974 xx o|||| 00||| eng d | ||
| 020 | |a 9781461298557 |c Online |9 978-1-4612-9855-7 | ||
| 020 | |a 9780387900940 |c Print |9 978-0-387-90094-0 | ||
| 024 | 7 | |a 10.1007/978-1-4612-9855-7 |2 doi | |
| 035 | |a (OCoLC)863802902 | ||
| 035 | |a (DE-599)BVBBV042420490 | ||
| 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 511.3 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Halmos, Paul R. |d 1916-2006 |e Verfasser |0 (DE-588)118746677 |4 aut | |
| 245 | 1 | 0 | |a Lectures on Boolean Algebras |c by Paul R. Halmos |
| 264 | 1 | |a New York, NY |b Springer New York |c 1974 | |
| 300 | |a 1 Online-Ressource (VIII, 148 p) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Undergraduate Texts in Mathematics |x 0172-6056 | |
| 500 | |a IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised. Most of the corrections were suggested by Peter Crawley. To judge by his detailed and precise suggestions, he must have read every word, checked every reference, and weighed every argument, and I am very grateful to hirn for his help. This is not to say that he is to be held responsible for the imperfections that remain, and, in particular, I alone am responsible for all expressions of personal opinion and irreverent viewpoint. P. R. H. Ann Arbor, Michigan January, 1963 Contents Section Page 1 1 Boolean rings ............................ . 2 Boolean algebras ......................... . 3 9 3 Fields of sets ............................ . 4 Regular open sets . . . . . . . . . . . . . . . . . . . 12 . . . . . . 5 Elementary relations. . . . . . . . . . . | ||
| 500 | |a . . . . . . . 17 . . . . . 6 Order. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . 7 Infinite operations. . .. . . . . . . . . . . . . . . . . 25 . . . . . 8 Subalgebras . . . . . . . . . . . . . . . . . . . . .. . . . 31 . . . . . . 9 Homomorphisms . . . . . . . . . . . . . . . . . . . . 35 . . . . . . . 10 Free algebras . . . . . . . . . . . . . . . . . . . . . . 40 . . . . . . . 11 Ideals and filters. . . . . . . . . . . . . . . . . . . . 47 . . . . . . 12 The homomorphism theorem. . . . . . . . . . . . .. . . 52 . . 13 Boolean a-algebras . . . . . . . . . . . . . . . . . . 55 . . . . . . 14 The countable chain condition . . . . . . . . . . . . 61 . . . 15 Measure algebras . . . . . . . . . . . . . . . . . . . 64 . . . . . . . 16 Atoms.. . . . .. . . . . .. .. . . . ... . . . . .. . . ... . . .. 69 17 Boolean spaces . . . . . . . . . . . . . . . . . . . . 72 . . . . . . . 18 The representation theorem. . . . . . . . . . . . . . 77 . . . | ||
| 500 | |a 19 Duality for ideals . . . . . . . . . . . . . . . . . .. . . 81 . . . . . 20 Duality for homomorphisms . . . . . . . . . . . . . . 84 . . . . 21 Completion . . . . . . . . . . . . . . . . . . . . . . . 90 . . . . . . . . 22 Boolean a-spaces . . . . . . . . . . . . . . . . . .. . . 97 . . . . . 23 The representation of a-algebras . . . . . . . . .. . . 100 . 24 Boolean measure spaces . . . . . . . . . . . . . .. . . 104 . . . 25 Incomplete algebras . . . . . . . . . . . . . . . .. . . 109 . . . . . 26 Products of algebras . . . . . . . . . . . . . . . .. . . 115 . . . . 27 Sums of algebras . . . . . . . . . . . . . . . . . .. . . 119 . . . . . 28 Isomorphisms of factors . . . . . . . . . . . . . .. . . 122 . . | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Mathematical Logic and Foundations | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Boolescher Verband |0 (DE-588)4146289-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Boolesche Algebra |0 (DE-588)4146280-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Boolescher Verband |0 (DE-588)4146289-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Boolesche Algebra |0 (DE-588)4146280-4 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-9855-7 |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:BVB01-027855907 | |
Datensatz im Suchindex
| DE-BY-TUM_katkey | 2067499 |
|---|---|
| _version_ | 1820806723484516352 |
| any_adam_object | |
| author | Halmos, Paul R. 1916-2006 |
| author_GND | (DE-588)118746677 |
| author_facet | Halmos, Paul R. 1916-2006 |
| author_role | aut |
| author_sort | Halmos, Paul R. 1916-2006 |
| author_variant | p r h pr prh |
| building | Verbundindex |
| bvnumber | BV042420490 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863802902 (DE-599)BVBBV042420490 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-9855-7 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04552nam a2200541zc 4500</leader><controlfield tag="001">BV042420490</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20211012 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1974 xx o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461298557</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-9855-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387900940</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-90094-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-9855-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863802902</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420490</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">511.3</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">Halmos, Paul R.</subfield><subfield code="d">1916-2006</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)118746677</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lectures on Boolean Algebras</subfield><subfield code="c">by Paul R. Halmos</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer New York</subfield><subfield code="c">1974</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (VIII, 148 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="0" ind2=" "><subfield code="a">Undergraduate Texts in Mathematics</subfield><subfield code="x">0172-6056</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">IN 1959 I lectured on Boolean algebras at the University of Chicago. A mimeographed version of the notes on which the lectures were based circulated for about two years; this volume contains those notes, corrected and revised. Most of the corrections were suggested by Peter Crawley. To judge by his detailed and precise suggestions, he must have read every word, checked every reference, and weighed every argument, and I am very grateful to hirn for his help. This is not to say that he is to be held responsible for the imperfections that remain, and, in particular, I alone am responsible for all expressions of personal opinion and irreverent viewpoint. P. R. H. Ann Arbor, Michigan January, 1963 Contents Section Page 1 1 Boolean rings ............................ . 2 Boolean algebras ......................... . 3 9 3 Fields of sets ............................ . 4 Regular open sets . . . . . . . . . . . . . . . . . . . 12 . . . . . . 5 Elementary relations. . . . . . . . . . .</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">. . . . . . . 17 . . . . . 6 Order. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . 7 Infinite operations. . .. . . . . . . . . . . . . . . . . 25 . . . . . 8 Subalgebras . . . . . . . . . . . . . . . . . . . . .. . . . 31 . . . . . . 9 Homomorphisms . . . . . . . . . . . . . . . . . . . . 35 . . . . . . . 10 Free algebras . . . . . . . . . . . . . . . . . . . . . . 40 . . . . . . . 11 Ideals and filters. . . . . . . . . . . . . . . . . . . . 47 . . . . . . 12 The homomorphism theorem. . . . . . . . . . . . .. . . 52 . . 13 Boolean a-algebras . . . . . . . . . . . . . . . . . . 55 . . . . . . 14 The countable chain condition . . . . . . . . . . . . 61 . . . 15 Measure algebras . . . . . . . . . . . . . . . . . . . 64 . . . . . . . 16 Atoms.. . . . .. . . . . .. .. . . . ... . . . . .. . . ... . . .. 69 17 Boolean spaces . . . . . . . . . . . . . . . . . . . . 72 . . . . . . . 18 The representation theorem. . . . . . . . . . . . . . 77 . . .</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">19 Duality for ideals . . . . . . . . . . . . . . . . . .. . . 81 . . . . . 20 Duality for homomorphisms . . . . . . . . . . . . . . 84 . . . . 21 Completion . . . . . . . . . . . . . . . . . . . . . . . 90 . . . . . . . . 22 Boolean a-spaces . . . . . . . . . . . . . . . . . .. . . 97 . . . . . 23 The representation of a-algebras . . . . . . . . .. . . 100 . 24 Boolean measure spaces . . . . . . . . . . . . . .. . . 104 . . . 25 Incomplete algebras . . . . . . . . . . . . . . . .. . . 109 . . . . . 26 Products of algebras . . . . . . . . . . . . . . . .. . . 115 . . . . 27 Sums of algebras . . . . . . . . . . . . . . . . . .. . . 119 . . . . . 28 Isomorphisms of factors . . . . . . . . . . . . . .. . . 122 . .</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical Logic and Foundations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</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="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="689" ind1="0" 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="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">Boolesche Algebra</subfield><subfield code="0">(DE-588)4146280-4</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="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-9855-7</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:BVB01-027855907</subfield></datafield></record></collection> |
| id | DE-604.BV042420490 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-24T04:23:21Z |
| institution | BVB |
| isbn | 9781461298557 9780387900940 |
| issn | 0172-6056 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855907 |
| oclc_num | 863802902 |
| 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 (VIII, 148 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Undergraduate Texts in Mathematics |
| spellingShingle | Halmos, Paul R. 1916-2006 Lectures on Boolean Algebras Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Boolescher Verband (DE-588)4146289-0 gnd Boolesche Algebra (DE-588)4146280-4 gnd |
| subject_GND | (DE-588)4146289-0 (DE-588)4146280-4 |
| title | Lectures on Boolean Algebras |
| title_auth | Lectures on Boolean Algebras |
| title_exact_search | Lectures on Boolean Algebras |
| title_full | Lectures on Boolean Algebras by Paul R. Halmos |
| title_fullStr | Lectures on Boolean Algebras by Paul R. Halmos |
| title_full_unstemmed | Lectures on Boolean Algebras by Paul R. Halmos |
| title_short | Lectures on Boolean Algebras |
| title_sort | lectures on boolean algebras |
| topic | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Boolescher Verband (DE-588)4146289-0 gnd Boolesche Algebra (DE-588)4146280-4 gnd |
| topic_facet | Mathematics Logic, Symbolic and mathematical Mathematical Logic and Foundations Mathematik Boolescher Verband Boolesche Algebra |
| url | https://doi.org/10.1007/978-1-4612-9855-7 |
| work_keys_str_mv | AT halmospaulr lecturesonbooleanalgebras |