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master's thesis
Odabrana poglavlja teorije kontinuuma
2023. urn:nbn:hr:166:880073
Maleš, Antonia
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Maleš, A. (2023). Odabrana poglavlja teorije kontinuuma (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:880073

Maleš, Antonia. "Odabrana poglavlja teorije kontinuuma." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:880073

Maleš, Antonia. "Odabrana poglavlja teorije kontinuuma." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:880073

Maleš, A. (2023). 'Odabrana poglavlja teorije kontinuuma', Master's thesis, University of Split, Faculty of Science, accessed 13 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:880073

Maleš A. Odabrana poglavlja teorije kontinuuma [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 November 13] Available at: https://urn.nsk.hr/urn:nbn:hr:166:880073

A. Maleš, "Odabrana poglavlja teorije kontinuuma", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:880073

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Metadata
TitleOdabrana poglavlja teorije kontinuuma
Title (english)Selected chapters of continuum theory
AuthorAntonia Maleš
MentorGoran Erceg (mentor)
Committee memberGoran Erceg (predsjednik povjerenstva)
Committee memberIvan Jelić (član povjerenstva)
Committee memberTanja Vojković (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-12-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Kontinuum je neprazan, povezan i kompaktan metrički prostor. Može biti rastavljiv ili nerastavljiv. Cilj ovog rada je proučiti tri osnovne metode kojima se od jednostavnijih primjera kontinuuma mogu konstruirati složeniji. Prva je metoda ugniježđenih presjeka, a ključan rezultat koji omogućuje njeno korištenje tvrdi da je ugniježđeni presjek kontinuuma također kontinuum. Druga je metoda inverznih limesa, za koju se pokaže da je poseban slučaj ugniježđenih presjeka. Dodatno se opisuju nerastavljivi inverzni nizovi čiji inverzni limesi daju nerastavljive kontinuume. Treća metoda je dekompozicija kontinuuma čija je ideja da se od particije kontinuuma dobije novi kontinuum. Pokaže se da to uvijek vrijedi za posebnu klasu takozvanih usc dekompozicija. Za sve metode navode se primjeri kontinuuma koji se pomoću njih konstruiraju.
Abstract (english)
A continuum is a nonempty, compact and connected metric space. It can be decomposable or indecomposable. The objective of this thesis is to describe three main methods for constructing complex examples of continuua from simpler ones. The first method uses nested intersections. The key to using this method lies in proving that the nested intersection of continua is a continuum. Second method uses inverse limits, which we prove to be a special case of nested intersections. Additionally, we describe indecomposable inverse sequences, whose inverse limits form indecomposable continua. Third method is the decomposition of continua. The idea is to obtain a new continuum using a partition of the given one. We show that this is always the case for a special class of so-called usc decompositions. For each method we give examples of continua constructed by them.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:880073
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in statistics and computing
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 on2024-01-15 13:07:36