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master's thesis
Topološka dimenzija
Zagreb: University of Zagreb, Faculty of Science, 2023. urn:nbn:hr:217:618214
Lončar, Nikolina
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Lončar, N. (2023). Topološka dimenzija (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:618214

Lončar, Nikolina. "Topološka dimenzija." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:618214

Lončar, Nikolina. "Topološka dimenzija." Master's thesis, University of Zagreb, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:217:618214

Lončar, N. (2023). 'Topološka dimenzija', Master's thesis, University of Zagreb, Faculty of Science, accessed 12 September 2024, https://urn.nsk.hr/urn:nbn:hr:217:618214

Lončar N. Topološka dimenzija [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2023 [cited 2024 September 12] Available at: https://urn.nsk.hr/urn:nbn:hr:217:618214

N. Lončar, "Topološka dimenzija", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:217:618214

Metadata
TitleTopološka dimenzija
Title (english)Topological dimension
AuthorNikolina Lončar
MentorZvonko Iljazović (mentor)
MentorVera Tonić (sumentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberNela Bosner (član povjerenstva)
Committee memberMarko Horvat (član povjerenstva)
Committee memberMatija Kazalicki (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2023-09-22, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu bavimo se topološkom dimenzijom kao svojstvom topoloških prostora. Nakon preliminarnih rezultata predstavljenih u prvom poglavlju, u drugom poglavlju uvodimo definiciju male induktivne dimenzije ind te dokazujemo ključne teoreme kao što su prvi i drugi teorem separacije i teorem sume. Veliku induktivnu dimenziju ind uvodimo u trećem poglavlju te proučavamo odnos male i velike induktivne dimenzije. Naposljetku, u četvrtom poglavlju uvodimo dimenziju pokrivanja te proučavamo odnos spomenutih dimenzija u slučaju separabilnog metričkog prostora.
Abstract (english)
In this paper, we study topological dimension as the property of topological spaces. After the preliminary notations assembled in Chapter 1, in Chapter 2 we introduce the definition of the small inductive dimension ind together with proofs of main theorems such as the first and the second separation theorem and the sum theorem. Chapter 3 deals with the large inductive dimension and the relation between the small and the large inductive dimension. Finally, in Chapter 4 we introduce the definition of the covering dimension and investigate the correlation between all of the mentioned dimensions in case of separable metric space.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:618214
Study programmeTitle: Theoretical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2024-02-02 09:48:09