Pituusavaruudet ja geodeesiset avaruudet

Tutkielma käsittelee polun pituutta metrisessä avaruudessa. Polun pituuden kautta määritellään käsitteet pituusavaruus ja geodeesinen avaruus. Työn päätulos on Hopfin ja Rinowin lause: lokaalisti kompaktissa täydellisessä pituusavaruudessa kaikki suljetut ja rajoitetut joukot ovat kompakteja, lisäks...

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Main Author: Järvinen, Janne
Other Authors: Matemaattis-luonnontieteellinen tiedekunta, Faculty of Sciences, Matematiikan ja tilastotieteen laitos, Department of Mathematics and Statistics, Jyväskylän yliopisto, University of Jyväskylä
Format: Master's thesis
Language:fin
Published: 2018
Subjects:
Online Access: https://jyx.jyu.fi/handle/123456789/59899
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author Järvinen, Janne
author2 Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics Jyväskylän yliopisto University of Jyväskylä
author_facet Järvinen, Janne Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics Jyväskylän yliopisto University of Jyväskylä Järvinen, Janne Matemaattis-luonnontieteellinen tiedekunta Faculty of Sciences Matematiikan ja tilastotieteen laitos Department of Mathematics and Statistics Jyväskylän yliopisto University of Jyväskylä
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description Tutkielma käsittelee polun pituutta metrisessä avaruudessa. Polun pituuden kautta määritellään käsitteet pituusavaruus ja geodeesinen avaruus. Työn päätulos on Hopfin ja Rinowin lause: lokaalisti kompaktissa täydellisessä pituusavaruudessa kaikki suljetut ja rajoitetut joukot ovat kompakteja, lisäksi mainituin ehdoin varustettu avaruus on geodeesinen.
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spellingShingle Järvinen, Janne Pituusavaruudet ja geodeesiset avaruudet polun pituus pituusavaruus polkumetriikka geodeesinen avaruus geodeesi Arzelàn ja Ascolin lause Hopfin ja Rinowin lause Matematiikka Mathematics 4041
title Pituusavaruudet ja geodeesiset avaruudet
title_full Pituusavaruudet ja geodeesiset avaruudet
title_fullStr Pituusavaruudet ja geodeesiset avaruudet Pituusavaruudet ja geodeesiset avaruudet
title_full_unstemmed Pituusavaruudet ja geodeesiset avaruudet Pituusavaruudet ja geodeesiset avaruudet
title_short Pituusavaruudet ja geodeesiset avaruudet
title_sort pituusavaruudet ja geodeesiset avaruudet
title_txtP Pituusavaruudet ja geodeesiset avaruudet
topic polun pituus pituusavaruus polkumetriikka geodeesinen avaruus geodeesi Arzelàn ja Ascolin lause Hopfin ja Rinowin lause Matematiikka Mathematics 4041
topic_facet 4041 Arzelàn ja Ascolin lause Hopfin ja Rinowin lause Matematiikka Mathematics geodeesi geodeesinen avaruus pituusavaruus polkumetriikka polun pituus
url https://jyx.jyu.fi/handle/123456789/59899 http://www.urn.fi/URN:NBN:fi:jyu-201810224481
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