Varieties of continua: from regions to points and back
Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform fra...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Oxford University Press
2018
|
| Ausgabe: | First edition |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts |
| Beschreibung: | This edition previously issued in print: 2018 |
| ISBN: | 9780191781087 |
| DOI: | 10.1093/oso/9780198712749.001.0001 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV045167606 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 180905s2018 |||| o||u| ||||||eng d | ||
| 020 | |a 9780191781087 |c Online |9 978-0-19-178108-7 | ||
| 024 | 7 | |a 10.1093/oso/9780198712749.001.0001 |2 doi | |
| 035 | |a (ZDB-28-OSP)EDZ0001840886 | ||
| 035 | |a (OCoLC)1051241238 | ||
| 035 | |a (DE-599)BVBBV045167606 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 082 | 0 | |a 515.222 |2 23 | |
| 084 | |a CC 2600 |0 (DE-625)17610: |2 rvk | ||
| 100 | 1 | |a Hellman, Geoffrey |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Varieties of continua |b from regions to points and back |c Geoffrey Hellman and Stewart Shapiro |
| 250 | |a First edition | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2018 | |
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a This edition previously issued in print: 2018 | ||
| 505 | 8 | |a Includes bibliographical references and index | |
| 520 | |a Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts | ||
| 650 | 4 | |a Continuity | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kontinuum |0 (DE-588)4032295-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kontinuum |0 (DE-588)4032295-6 |D s |
| 689 | 0 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Shapiro, Stewart |d 1951- |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9780198712749 |
| 856 | 4 | 0 | |u https://doi.org/10.1093/oso/9780198712749.001.0001 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 912 | |a ZDB-28-OSP | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-030556981 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804178853168414720 |
|---|---|
| any_adam_object | |
| author | Hellman, Geoffrey Shapiro, Stewart 1951- |
| author_facet | Hellman, Geoffrey Shapiro, Stewart 1951- |
| author_role | aut aut |
| author_sort | Hellman, Geoffrey |
| author_variant | g h gh s s ss |
| building | Verbundindex |
| bvnumber | BV045167606 |
| classification_rvk | CC 2600 |
| collection | ZDB-28-OSP |
| contents | Includes bibliographical references and index |
| ctrlnum | (ZDB-28-OSP)EDZ0001840886 (OCoLC)1051241238 (DE-599)BVBBV045167606 |
| dewey-full | 515.222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.222 |
| dewey-search | 515.222 |
| dewey-sort | 3515.222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| doi_str_mv | 10.1093/oso/9780198712749.001.0001 |
| edition | First edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02536nmm a2200457zc 4500</leader><controlfield tag="001">BV045167606</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">180905s2018 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780191781087</subfield><subfield code="c">Online</subfield><subfield code="9">978-0-19-178108-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1093/oso/9780198712749.001.0001</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-28-OSP)EDZ0001840886</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1051241238</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV045167606</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="082" ind1="0" ind2=" "><subfield code="a">515.222</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CC 2600</subfield><subfield code="0">(DE-625)17610:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hellman, Geoffrey</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Varieties of continua</subfield><subfield code="b">from regions to points and back</subfield><subfield code="c">Geoffrey Hellman and Stewart Shapiro</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">First edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Oxford</subfield><subfield code="b">Oxford University Press</subfield><subfield code="c">2018</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="500" ind1=" " ind2=" "><subfield code="a">This edition previously issued in print: 2018</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continuity</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kontinuum</subfield><subfield code="0">(DE-588)4032295-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kontinuum</subfield><subfield code="0">(DE-588)4032295-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</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="700" ind1="1" ind2=" "><subfield code="a">Shapiro, Stewart</subfield><subfield code="d">1951-</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9780198712749</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1093/oso/9780198712749.001.0001</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-28-OSP</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030556981</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></record></collection> |
| id | DE-604.BV045167606 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:10:34Z |
| institution | BVB |
| isbn | 9780191781087 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030556981 |
| oclc_num | 1051241238 |
| open_access_boolean | |
| psigel | ZDB-28-OSP |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Oxford University Press |
| record_format | marc |
| spelling | Hellman, Geoffrey Verfasser aut Varieties of continua from regions to points and back Geoffrey Hellman and Stewart Shapiro First edition Oxford Oxford University Press 2018 txt rdacontent c rdamedia cr rdacarrier This edition previously issued in print: 2018 Includes bibliographical references and index Two historical episodes form the background to the research presented here: the first is the remarkably rapid transition in the course of the nineteenth century from the ancient Aristotelian view that a true continuum cannot be composed entirely of points to the now standard, entirely punctiform frameworks for analysis and geometry found in modern texts. The second is the mid-to-late 20th-century revival of pre-limit methods in analysis and geometry using infinitesimals, viz. non-standard analysis due to Abraham Robinson, and the more radical smooth infinitesimal analysis based on intuitionistic logic. One goal of this work is to develop a systematic comparison of these. A second goal is to develop thoroughgoing regions-based theories of classical continua that are mathematically equivalent to the currently standard, punctiform accounts of modern texts Continuity Mathematik (DE-588)4037944-9 gnd rswk-swf Kontinuum (DE-588)4032295-6 gnd rswk-swf Kontinuum (DE-588)4032295-6 s Mathematik (DE-588)4037944-9 s 1\p DE-604 Shapiro, Stewart 1951- aut Erscheint auch als Druck-Ausgabe 9780198712749 https://doi.org/10.1093/oso/9780198712749.001.0001 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hellman, Geoffrey Shapiro, Stewart 1951- Varieties of continua from regions to points and back Includes bibliographical references and index Continuity Mathematik (DE-588)4037944-9 gnd Kontinuum (DE-588)4032295-6 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4032295-6 |
| title | Varieties of continua from regions to points and back |
| title_auth | Varieties of continua from regions to points and back |
| title_exact_search | Varieties of continua from regions to points and back |
| title_full | Varieties of continua from regions to points and back Geoffrey Hellman and Stewart Shapiro |
| title_fullStr | Varieties of continua from regions to points and back Geoffrey Hellman and Stewart Shapiro |
| title_full_unstemmed | Varieties of continua from regions to points and back Geoffrey Hellman and Stewart Shapiro |
| title_short | Varieties of continua |
| title_sort | varieties of continua from regions to points and back |
| title_sub | from regions to points and back |
| topic | Continuity Mathematik (DE-588)4037944-9 gnd Kontinuum (DE-588)4032295-6 gnd |
| topic_facet | Continuity Mathematik Kontinuum |
| url | https://doi.org/10.1093/oso/9780198712749.001.0001 |
| work_keys_str_mv | AT hellmangeoffrey varietiesofcontinuafromregionstopointsandback AT shapirostewart varietiesofcontinuafromregionstopointsandback |