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master's thesis
Topološki digitalni prostori
2023. urn:nbn:hr:166:384492
Grbeša Dragun, Ivona
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Grbeša Dragun, I. (2023). Topološki digitalni prostori (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:384492

Grbeša Dragun, Ivona. "Topološki digitalni prostori." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:384492

Grbeša Dragun, Ivona. "Topološki digitalni prostori." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:384492

Grbeša Dragun, I. (2023). 'Topološki digitalni prostori', Master's thesis, University of Split, Faculty of Science, accessed 24 April 2024, https://urn.nsk.hr/urn:nbn:hr:166:384492

Grbeša Dragun I. Topološki digitalni prostori [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2024 April 24] Available at: https://urn.nsk.hr/urn:nbn:hr:166:384492

I. Grbeša Dragun, "Topološki digitalni prostori", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:384492

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Metadata
TitleTopološki digitalni prostori
Title (english)Topological digital spaces
AuthorIvona Grbeša Dragun
MentorGoran Erceg (mentor)
Committee memberGoran Erceg (predsjednik povjerenstva)
Committee memberDino Peran (član povjerenstva)
Committee memberDomagoj Jelić (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-09-21, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu predstavljeni su glavni rezultati teorije topoloških digitalnih prostora. Topološki digitalni prostori su klasa topoloških prostora u kojima se, uz odgovarajuće prilagodbe, povezanost piksela može definirati pomoću topološke povezanosti. U prvom dijelu rada definiramo digitalne prostore, topološke digitalne prostore i Aleksandrovljeve topološke prostore te iskazujemo njihova svojstva, uz poseban naglasak na Khalimskyjeve prostore. Drugi dio rada posvećen je neprekidnim funkcijama na Khalimskyjevom prostoru te se razmatra problem njihove neprekidne proširivosti. Na samom kraju uvodimo pojam graf-povezanih skupova, koji imaju ulogu u dobivanju jednog od najvažnijih rezultata, a to je digitalni analogon Tietzeovog teorema o proširenju.
Abstract (english)
This thesis presents the main results of the theory of topological digital spaces. Topological digital spaces are a class of topological spaces in which, with appropriate adjustments, the connectivity of pixels can be defined using topological connectedness. In the first part we define digital spaces, topological digital spaces and Alexandrov topological spaces and we state their properties, with special emphasis on Khalimsky spaces. The second part is devoted to continuous functions on the Khalimsky space and it discusses the problem of their continuous extension. Finally, we introduce the concept of graph-connected sets, which play a role in obtaining one of the most important results, the digital analog of the Tietze extension theorem.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:384492
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 Attribution 4.0 International (CC BY 4.0) icon
Created on2023-09-26 07:45:13