prikaz prve stranice dokumenta Zornova lema i srodne tvrdnje
  Download
PDF 265.42 KB
master's thesis
Zornova lema i srodne tvrdnje
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:663843
Gunja, Marin
University of Zagreb
Faculty of Science

Institutional repository: Repository of the Faculty of Science

Cite this document

Gunja, M. (2020). Zornova lema i srodne tvrdnje (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:663843

Gunja, Marin. "Zornova lema i srodne tvrdnje." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:663843

Gunja, Marin. "Zornova lema i srodne tvrdnje." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:663843

Gunja, M. (2020). 'Zornova lema i srodne tvrdnje', Master's thesis, University of Zagreb, Faculty of Science, accessed 17 June 2024, https://urn.nsk.hr/urn:nbn:hr:217:663843

Gunja M. Zornova lema i srodne tvrdnje [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 June 17] Available at: https://urn.nsk.hr/urn:nbn:hr:217:663843

M. Gunja, "Zornova lema i srodne tvrdnje", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:663843

Metadata
TitleZornova lema i srodne tvrdnje
AuthorMarin Gunja
MentorVedran Čačić (mentor)
Committee memberVedran Čačić (predsjednik povjerenstva)
Committee memberMarko Horvat (član povjerenstva)
Committee memberMladen Vuković (član povjerenstva)
Committee memberZvonko Iljazović (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
Zagreb
Defense date and country2020-07-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ukratko, u ovome radu se bavimo Zornovom lemom i srodnim tvrdnjama. U uvodu je obrazlo ženo zašto je naglasak na Zornovoj lemi. U prvom poglavlju je precizno iskazan aksiom izbora, nabrojane su neke njemu ekvivalentne tvrdnje i neke njegove posljedice. Navedene su i neke posljedice aksioma izbora iz raznih grana matematike (linearne algebre, topologije, analize, i tako dalje). U drugom poglavlju najprije definiramo pojmove potrebne za razumijevanje iskaza Zornove leme (parcijalno ureden skup, lanac, i slično). Nakon toga precizno iskazujemo Zornovu lemu, te je dokazujemo pod pretpostavkom aksioma izbora. Osim toga, iznosimo i nekoliko primjera upotrebe Zornove leme. U trećem poglavlju se bavimo još jednim važnim teoremom teorije skupova: Zermelovim teoremom o dobrom uredaju. Preciznije, dokazujemo da Zornova lema povlači Zermelov teorem o dobrom uredaju. Na kraju poglavlja dokazujemo da Zermelov teorem povlači aksiom izbora.
Abstract (english)
In this paper, we present Zorn’s lemma and some of its related statements. The introduction explains why the emphasis is on Zorn’s lemma. In the first chapter, we state the axiom of choice with some of its equivalent statements and consequences. We also state some consequences of axiom of choice from various branches of mathematics (linear algebra, topology, analysis, and so on). In the second chapter we first define some terms which are needed to understand the statement of Zorn’s lemma (partially ordered set, chain, and so on). Afterwards, we give a precise statement of Zorn’s lemma and we prove it assuming the axiom of choice. We also provide a few examples of how Zorn’s lemma can be used. In the third chapter, we present another important theorem of set theory: the wellordering theorem. We prove that Zorn’s lemma implies the well-ordering theorem. At the end of this chapter, we prove that the well-ordering theorem implies the axiom of choice.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:663843
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-11-25 11:31:02