Partially ordered rings and semi-algebraic geometry:
The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1979
|
| Schriftenreihe: | London Mathematical Society lecture note series
37 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (280 pages) |
| ISBN: | 9780511721533 |
| DOI: | 10.1017/CBO9780511721533 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV043942293 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 161206s1979 |||| o||u| ||||||eng d | ||
| 020 | |a 9780511721533 |c Online |9 978-0-511-72153-3 | ||
| 024 | 7 | |a 10.1017/CBO9780511721533 |2 doi | |
| 035 | |a (ZDB-20-CBO)CR9780511721533 | ||
| 035 | |a (OCoLC)849796867 | ||
| 035 | |a (DE-599)BVBBV043942293 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-92 | ||
| 082 | 0 | |a 512.4 |2 19eng | |
| 084 | |a SI 320 |0 (DE-625)143123: |2 rvk | ||
| 084 | |a SK 240 |0 (DE-625)143226: |2 rvk | ||
| 100 | 1 | |a Brumfiel, Gregory W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Partially ordered rings and semi-algebraic geometry |c Gregory W. Brumfiel |
| 246 | 1 | 3 | |a Partially Ordered Rings & Semi-Algebraic Geometry |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1979 | |
| 300 | |a 1 online resource (280 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a London Mathematical Society lecture note series |v 37 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance | ||
| 650 | 4 | |a Commutative rings | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 0 | 7 | |a Geordneter Ring |0 (DE-588)4156754-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Semialgebraischer Raum |0 (DE-588)4116475-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Semialgebraischer Raum |0 (DE-588)4116475-1 |D s |
| 689 | 0 | 1 | |a Geordneter Ring |0 (DE-588)4156754-7 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druckausgabe |z 978-0-521-22845-9 |
| 856 | 4 | 0 | |u https://doi.org/10.1017/CBO9780511721533 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-20-CBO | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-029351262 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511721533 |l BSB01 |p ZDB-20-CBO |q BSB_PDA_CBO |x Verlag |3 Volltext | |
| 966 | e | |u https://doi.org/10.1017/CBO9780511721533 |l FHN01 |p ZDB-20-CBO |q FHN_PDA_CBO |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804176884941979648 |
|---|---|
| any_adam_object | |
| author | Brumfiel, Gregory W. |
| author_facet | Brumfiel, Gregory W. |
| author_role | aut |
| author_sort | Brumfiel, Gregory W. |
| author_variant | g w b gw gwb |
| building | Verbundindex |
| bvnumber | BV043942293 |
| classification_rvk | SI 320 SK 240 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511721533 (OCoLC)849796867 (DE-599)BVBBV043942293 |
| dewey-full | 512.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.4 |
| dewey-search | 512.4 |
| dewey-sort | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511721533 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03220nmm a2200517zcb4500</leader><controlfield tag="001">BV043942293</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">161206s1979 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511721533</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-511-72153-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1017/CBO9780511721533</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-20-CBO)CR9780511721533</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)849796867</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043942293</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512.4</subfield><subfield code="2">19eng</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 320</subfield><subfield code="0">(DE-625)143123:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 240</subfield><subfield code="0">(DE-625)143226:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Brumfiel, Gregory W.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Partially ordered rings and semi-algebraic geometry</subfield><subfield code="c">Gregory W. Brumfiel</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Partially Ordered Rings & Semi-Algebraic Geometry</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="b">Cambridge University Press</subfield><subfield code="c">1979</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (280 pages)</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">London Mathematical Society lecture note series</subfield><subfield code="v">37</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Title from publisher's bibliographic system (viewed on 05 Oct 2015)</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Commutative rings</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Categories (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geordneter Ring</subfield><subfield code="0">(DE-588)4156754-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Semialgebraischer Raum</subfield><subfield code="0">(DE-588)4116475-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Semialgebraischer Raum</subfield><subfield code="0">(DE-588)4116475-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Geordneter Ring</subfield><subfield code="0">(DE-588)4156754-7</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="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druckausgabe</subfield><subfield code="z">978-0-521-22845-9</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1017/CBO9780511721533</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-20-CBO</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-029351262</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="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721533</subfield><subfield code="l">BSB01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">BSB_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1017/CBO9780511721533</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-20-CBO</subfield><subfield code="q">FHN_PDA_CBO</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043942293 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511721533 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351262 |
| oclc_num | 849796867 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (280 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Brumfiel, Gregory W. Verfasser aut Partially ordered rings and semi-algebraic geometry Gregory W. Brumfiel Partially Ordered Rings & Semi-Algebraic Geometry Cambridge Cambridge University Press 1979 1 online resource (280 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 37 Title from publisher's bibliographic system (viewed on 05 Oct 2015) The purpose of this unique book is to establish purely algebraic foundations for the development of certain parts of topology. Some topologists seek to understand geometric properties of solutions to finite systems of equations or inequalities and configurations which in some sense actually occur in the real world. Others study spaces constructed more abstractly using infinite limit processes. Their goal is to determine just how similar or different these abstract spaces are from those which are finitely described. However, as topology is usually taught, even the first, more concrete type of problem is approached using the language and methods of the second type. Professor Brumfiel's thesis is that this is unnecessary and, in fact, misleading philosophically. He develops a type of algebra, partially ordered rings, in which it makes sense to talk about solutions of equations and inequalities and to compare geometrically the resulting spaces. The importance of this approach is primarily that it clarifies the sort of geometrical questions one wants to ask and answer about those spaces which might have physical significance Commutative rings Categories (Mathematics) Geordneter Ring (DE-588)4156754-7 gnd rswk-swf Semialgebraischer Raum (DE-588)4116475-1 gnd rswk-swf Semialgebraischer Raum (DE-588)4116475-1 s Geordneter Ring (DE-588)4156754-7 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-22845-9 https://doi.org/10.1017/CBO9780511721533 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Brumfiel, Gregory W. Partially ordered rings and semi-algebraic geometry Commutative rings Categories (Mathematics) Geordneter Ring (DE-588)4156754-7 gnd Semialgebraischer Raum (DE-588)4116475-1 gnd |
| subject_GND | (DE-588)4156754-7 (DE-588)4116475-1 |
| title | Partially ordered rings and semi-algebraic geometry |
| title_alt | Partially Ordered Rings & Semi-Algebraic Geometry |
| title_auth | Partially ordered rings and semi-algebraic geometry |
| title_exact_search | Partially ordered rings and semi-algebraic geometry |
| title_full | Partially ordered rings and semi-algebraic geometry Gregory W. Brumfiel |
| title_fullStr | Partially ordered rings and semi-algebraic geometry Gregory W. Brumfiel |
| title_full_unstemmed | Partially ordered rings and semi-algebraic geometry Gregory W. Brumfiel |
| title_short | Partially ordered rings and semi-algebraic geometry |
| title_sort | partially ordered rings and semi algebraic geometry |
| topic | Commutative rings Categories (Mathematics) Geordneter Ring (DE-588)4156754-7 gnd Semialgebraischer Raum (DE-588)4116475-1 gnd |
| topic_facet | Commutative rings Categories (Mathematics) Geordneter Ring Semialgebraischer Raum |
| url | https://doi.org/10.1017/CBO9780511721533 |
| work_keys_str_mv | AT brumfielgregoryw partiallyorderedringsandsemialgebraicgeometry AT brumfielgregoryw partiallyorderedringssemialgebraicgeometry |