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master's thesis
O dimenziji topološkog prostora
2017. urn:nbn:hr:166:071545
Olivari, Luca
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Olivari, L. (2017). O dimenziji topološkog prostora (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:071545

Olivari, Luca. "O dimenziji topološkog prostora." Master's thesis, University of Split, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:071545

Olivari, Luca. "O dimenziji topološkog prostora." Master's thesis, University of Split, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:166:071545

Olivari, L. (2017). 'O dimenziji topološkog prostora', Master's thesis, University of Split, Faculty of Science, accessed 19 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:071545

Olivari L. O dimenziji topološkog prostora [Master's thesis]. Split: University of Split, Faculty of Science; 2017 [cited 2024 November 19] Available at: https://urn.nsk.hr/urn:nbn:hr:166:071545

L. Olivari, "O dimenziji topološkog prostora", Master's thesis, University of Split, Faculty of Science, Split, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:166:071545

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Metadata
TitleO dimenziji topološkog prostora
Title (english)On dimension of topological space
AuthorLuca Olivari
MentorVlasta Matijević (mentor)
Committee memberVlasta Matijević (predsjednik povjerenstva)
Committee memberNikola Koceić Bilan (član povjerenstva)
Committee memberGoran Erceg (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2017-07-07, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu definiramo tri dimenzije topološkog prostora, malu induktivnu dimenziju, veliku induktivnu dimenziju i dimenziju pokrivanja, te dokazujemo neke važne teoreme o tim dimenzijama. Posebno, dokazujemo da se u klasi seprabilnih metrizabilnih prostora podudaraju sve tri dimenzije, te da se u klasi metrizabilnih prostora podudaraju velika induktivna dimenzija i dimenzija pokrivanja. Naposljetku, dokazujemo da je dimenzija euklidskog prostora Rn jednaka n, bilo da se radi o maloj induktivnoj dimenziji, velikoj induktivnoj dimenziji, ili dimenziji pokrivanja.
Abstract (english)
In this thesis we define three different dimensions of a topological space, small inductive dimension, large inductive dimension and covering dimension, and we prove some important theorems about these dimensions. In particular, we prove that the three dimensions coincide in the class of all separable metrizable spaces, while the large inductive dimension and the covering dimension coincide in the class of all metrizable spaces. Finally, we prove that the dimension of the Euclidean space Rn is equal to n, whether it is the small inductive dimension, the large inductive dimension, or the covering dimension.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:071545
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching
Course: major in pure mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-05-18 15:21:53