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master's thesis
Topološki aspekti aksioma potpunosti
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:597129
Volarić, Martina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Volarić, M. (2018). Topološki aspekti aksioma potpunosti (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:597129

Volarić, Martina. "Topološki aspekti aksioma potpunosti." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:597129

Volarić, Martina. "Topološki aspekti aksioma potpunosti." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:597129

Volarić, M. (2018). 'Topološki aspekti aksioma potpunosti', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:597129

Volarić M. Topološki aspekti aksioma potpunosti [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:597129

M. Volarić, "Topološki aspekti aksioma potpunosti", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:597129

Metadata
TitleTopološki aspekti aksioma potpunosti
AuthorMartina Volarić
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberSonja Štimac (član povjerenstva)
Committee memberMaja Resman (član povjerenstva)
Committee memberZrinka Franušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-07-17, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom diplomskom radu proučavamo neprekidne funkcije na segmentu, ali i topološke prostore i koncepte s tim u vezi pomoću kojih možemo dokazati neke klasične rezultate vezane za neprekidne funkcije na segmentu. U prvom poglavlju koristeći gomilište nizova dokazujemo da svaka neprekidna funkcija na segmentu poprima minimum i maksimum. U drugom poglavlju proučavamo pojmove topologije, baze topologije, neprekidnosti funkcije između topoloških prostora i relativne topologije. Također, proučavamo kompaktne skupove u topološkim prostorima te dokazujemo da neprekidne realne funkcije na kompaktnim prostorima poprimaju minimum i maksimum. U trećem poglavlju proučavamo povezanost u topološkim prostorima te dokazujemo da neprekidna realna funkcija na povezanom prostoru poprima međuvrijednosti.
Abstract (english)
In this thesis we have studied continuous functions on segment, topological spaces and related concepts which we use to prove some classical results related to continuous functions on a segment. In the first chapter we use that each continuous function on a segment attains its minimum and maximum. In the second chapter we study topological spaces, continuous functions between topological spaces and relative topologies. We also study compact sets in topological spaces and we prove that each continuous real function on a compact space attains its minimum and maximum. In the third chapter we examine connectedness in topological spaces and we prove that each continuous real function on a connected space attains intermediate values.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:597129
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-07-05 11:08:01