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master's thesis
Generalizirani inverzni limesi
2020. urn:nbn:hr:166:292659
Marić, Stipe
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Marić, S. (2020). Generalizirani inverzni limesi (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:292659

Marić, Stipe. "Generalizirani inverzni limesi." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:292659

Marić, Stipe. "Generalizirani inverzni limesi." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:292659

Marić, S. (2020). 'Generalizirani inverzni limesi', Master's thesis, University of Split, Faculty of Science, accessed 13 November 2024, https://urn.nsk.hr/urn:nbn:hr:166:292659

Marić S. Generalizirani inverzni limesi [Master's thesis]. Split: University of Split, Faculty of Science; 2020 [cited 2024 November 13] Available at: https://urn.nsk.hr/urn:nbn:hr:166:292659

S. Marić, "Generalizirani inverzni limesi", Master's thesis, University of Split, Faculty of Science, Split, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:166:292659

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Metadata
TitleGeneralizirani inverzni limesi
Title (english)Generalized inverse limits
AuthorStipe Marić
MentorGoran Erceg (mentor)
Committee memberGoran Erceg (predsjednik povjerenstva)
Committee memberNikola Koceić-Bilan (član povjerenstva)
Committee memberIvan Jelić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2020-08-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu obraduju se generalizirani inverzni limesi. Generalizirani inverzni limesi su poopćenje inverznih limesa u smislu da se u inverznom nizu, umjesto običnih funkcija, promatraju funkcije kojima su, za svaku točku iz domene funkcije, funkcijske vrijednosti skupovi. Prvo se definiraju odozgo poluneprekidne funkcije i iskazuju njena svojstva. Potom se definira generalizirani inverzni niz, a nakon toga i generalizirani inverzni limes. Nadalje, dokazuje se egzistencija i kompaktnost generaliziranog inverznog limesa. U drugom dijelu rada se ispituje povezanost generaliziranog inverznog limesa. Uspoređuje se odnos povezanosti generaliziranog inverznog limesa i grafova pripadnih funkcija, iskazuju karakterizacije i dovoljni uvjeti za povezanost. Na kraju se uvodi pojam topološke konjugacije i dokazuje teorem o uniji. Rad sadrži brojne primjere koji često pokazuju kako primijeniti dokazane teoreme ili pokazuju da obrati nekih teorema ne vrijede.
Abstract (english)
This thesis deals with generalized inverse limits. Generalized inverse limits are generalization of standard inverse limits in a way that in the corresponding inverse sequence, instead of ”ordinary” functions, we observe set-valued functions. In the first part we define upper semicontinous functions and we express its properties. We also define generalized inverse sequence and than generalized inverse limits. Further, we prove the existence and compactness of generalized inverse limit. In the second part we examine the connectedness of generalized inverse limit. The connectedness of generalized inverse limits is compared with the connectedness of graphs of corresponding functions, both characterization and sufficient conditions for connectedness are expressed too. We end with the notion of topological conjugacy and the proof of union theorem. This thesis contains many examples that often shows how to use proven theorems or shows that the reversals of some theorems are not valid.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:292659
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
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 conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2021-02-02 15:20:45