| fullrecord |
[{"key": "dc.contributor.advisor", "value": "Pankka, Pekka", "language": "", "element": "contributor", "qualifier": "advisor", "schema": "dc"}, {"key": "dc.contributor.author", "value": "Schultz, Timo", "language": null, "element": "contributor", "qualifier": "author", "schema": "dc"}, {"key": "dc.date.accessioned", "value": "2016-01-15T10:16:18Z", "language": "", "element": "date", "qualifier": "accessioned", "schema": "dc"}, {"key": "dc.date.available", "value": "2016-01-15T10:16:18Z", "language": "", "element": "date", "qualifier": "available", "schema": "dc"}, {"key": "dc.date.issued", "value": "2015", "language": null, "element": "date", "qualifier": "issued", "schema": "dc"}, {"key": "dc.identifier.other", "value": "oai:jykdok.linneanet.fi:1507366", "language": null, "element": "identifier", "qualifier": "other", "schema": "dc"}, {"key": "dc.identifier.uri", "value": "https://jyx.jyu.fi/handle/123456789/48361", "language": "", "element": "identifier", "qualifier": "uri", "schema": "dc"}, {"key": "dc.description.abstract", "value": "T\u00e4ss\u00e4 tutkielmassa osoitetaan ennest\u00e4\u00e4n tunnettu pintoihin liittyv\u00e4 tulos, jonka mukaan ep\u00e4kompaktin pinnan perusryhm\u00e4 on vapaa. Todistus\r\npohjautuu tietoon siit\u00e4, ett\u00e4 jokaisella pinnalla on olemassa niin sanottu\r\nkolmiointi. Pinnan kolmiointia hy\u00f6dynt\u00e4en pinta tyhjennet\u00e4\u00e4n sopivilla\r\nsis\u00e4kk\u00e4isill\u00e4 kompakteilla reunallisilla pinnoilla siten, ett\u00e4 pinnan perus\r\nryhm\u00e4 saadaan n\u00e4iden kompaktien reunallisten pintojen sis\u00e4kk\u00e4isten pe\r\nrusryhmien yhdisteen\u00e4. Kompakti reunallinen pinta osoitetaan homotopia\r\nekvivalentiksi graafin kanssa deformaatioretraktoimalla reunallinen pinta\r\ngraafiksi reunallisen pinnan kolmiointia hy\u00f6dynt\u00e4en. Koska homotopiaekvi\r\nvalenttien avaruuksien perusryhm\u00e4t ovat isomorfiset, saadaan kompaktin\r\nreunallisen pinnan perusryhm\u00e4 osoitettua vapaaksi osoittamalla, ett\u00e4 graafin perusryhm\u00e4 on vapaa ryhm\u00e4. Graafin perusryhm\u00e4 osoitetaan vapaaksi\r\nryhm\u00e4ksi k\u00e4ytt\u00e4en tietoa niin sanotun maksimaalisen puun olemassaolosta.\r\nTodistuksessa k\u00e4ytet\u00e4\u00e4n lis\u00e4ksi Van Kampenin teoreemaa, joka my\u00f6s todistetaan. Tutkielman tulos sanoo, ett\u00e4 esimerkiksi poistamalla kompaktilta\r\npinnalta topologinen Cantorin joukko saadaan pinta, jonka perusryhm\u00e4\r\non vapaa, mik\u00e4 itsess\u00e4\u00e4n ei ole intuitiivisesti selv\u00e4\u00e4.", "language": "fi", "element": "description", "qualifier": "abstract", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted using Plone Publishing form by Timo Schultz (timischu) on 2016-01-15 10:16:17.580919. Form: Pro gradu -lomake (https://kirjasto.jyu.fi/julkaisut/julkaisulomakkeet/pro-gradu-lomake). JyX data: [jyx_publishing-allowed (fi) =True]", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Submitted by jyx lomake-julkaisija (jyx-julkaisija.group@korppi.jyu.fi) on 2016-01-15T10:16:17Z\r\nNo. of bitstreams: 2\r\nURN:NBN:fi:jyu-201601151117.pdf: 674540 bytes, checksum: 73baba11ddf6482655da77cd0b346eb6 (MD5)\r\nlicense.html: 4777 bytes, checksum: 4295298f0803b19d5f57b06baaf1604b (MD5)", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.description.provenance", "value": "Made available in DSpace on 2016-01-15T10:16:18Z (GMT). No. of bitstreams: 2\r\nURN:NBN:fi:jyu-201601151117.pdf: 674540 bytes, checksum: 73baba11ddf6482655da77cd0b346eb6 (MD5)\r\nlicense.html: 4777 bytes, checksum: 4295298f0803b19d5f57b06baaf1604b (MD5)\r\n Previous issue date: 2015", "language": "en", "element": "description", "qualifier": "provenance", "schema": "dc"}, {"key": "dc.format.extent", "value": "1 verkkoaineisto (73 sivua)", "language": null, "element": "format", "qualifier": "extent", "schema": "dc"}, {"key": "dc.format.mimetype", "value": "application/pdf", "language": null, "element": "format", "qualifier": "mimetype", "schema": "dc"}, {"key": "dc.language.iso", "value": "fin", "language": null, "element": "language", "qualifier": "iso", "schema": "dc"}, {"key": "dc.rights", "value": "In Copyright", "language": "en", "element": "rights", "qualifier": null, "schema": "dc"}, {"key": "dc.subject.other", "value": "pinta", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "graafi", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "perusryhm\u00e4", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "vapaa ryhm\u00e4", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "homotopia", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "topologia", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.subject.other", "value": "algebrallinen topologia", "language": "", "element": "subject", "qualifier": "other", "schema": "dc"}, {"key": "dc.title", "value": "Pintojen perusryhmist\u00e4", "language": null, "element": "title", "qualifier": null, "schema": "dc"}, {"key": "dc.type", "value": "master thesis", "language": null, "element": "type", "qualifier": null, "schema": "dc"}, {"key": "dc.identifier.urn", "value": "URN:NBN:fi:jyu-201601151117", "language": null, "element": "identifier", "qualifier": "urn", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Pro gradu -tutkielma", "language": "fi", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.type.ontasot", "value": "Master\u2019s thesis", "language": "en", "element": "type", "qualifier": "ontasot", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Matemaattis-luonnontieteellinen tiedekunta", "language": "fi", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.faculty", "value": "Faculty of Sciences", "language": "en", "element": "contributor", "qualifier": "faculty", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Matematiikan ja tilastotieteen laitos", "language": "fi", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.department", "value": "Department of Mathematics and Statistics", "language": "en", "element": "contributor", "qualifier": "department", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "University of Jyv\u00e4skyl\u00e4", "language": "en", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.contributor.organization", "value": "Jyv\u00e4skyl\u00e4n yliopisto", "language": "fi", "element": "contributor", "qualifier": "organization", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Matematiikka", "language": "fi", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.subject.discipline", "value": "Mathematics", "language": "en", "element": "subject", "qualifier": "discipline", "schema": "dc"}, {"key": "dc.date.updated", "value": "2016-01-15T10:16:18Z", "language": "", "element": "date", "qualifier": "updated", "schema": "dc"}, {"key": "yvv.contractresearch.funding", "value": "0", "language": "", "element": "contractresearch", "qualifier": "funding", "schema": "yvv"}, {"key": "dc.type.coar", "value": "http://purl.org/coar/resource_type/c_bdcc", "language": null, "element": "type", "qualifier": "coar", "schema": "dc"}, {"key": "dc.rights.accesslevel", "value": "openAccess", "language": "fi", "element": "rights", "qualifier": "accesslevel", "schema": "dc"}, {"key": "dc.type.publication", "value": "masterThesis", "language": null, "element": "type", "qualifier": "publication", "schema": "dc"}, {"key": "dc.subject.oppiainekoodi", "value": "4041", "language": null, "element": "subject", "qualifier": "oppiainekoodi", "schema": "dc"}, {"key": "dc.subject.yso", "value": "pinnat", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "graafit", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "ryhm\u00e4t", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.subject.yso", "value": "topologia", "language": null, "element": "subject", "qualifier": "yso", "schema": "dc"}, {"key": "dc.format.content", "value": "fulltext", "language": null, "element": "format", "qualifier": "content", "schema": "dc"}, {"key": "dc.rights.url", "value": "https://rightsstatements.org/page/InC/1.0/", "language": null, "element": "rights", "qualifier": "url", "schema": "dc"}, {"key": "dc.type.okm", "value": "G2", "language": null, "element": "type", "qualifier": "okm", "schema": "dc"}]
|