prikaz prve stranice dokumenta Izračunljivi topološki prostori
  Download
PDF 282.77 KB
master's thesis
Izračunljivi topološki prostori
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:232132
Lijović, Marija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Lijović, M. (2015). Izračunljivi topološki prostori (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:232132

Lijović, Marija. "Izračunljivi topološki prostori." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:232132

Lijović, Marija. "Izračunljivi topološki prostori." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:232132

Lijović, M. (2015). 'Izračunljivi topološki prostori', Master's thesis, University of Zagreb, Faculty of Science, accessed 30 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:232132

Lijović M. Izračunljivi topološki prostori [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 November 30] Available at: https://urn.nsk.hr/urn:nbn:hr:217:232132

M. Lijović, "Izračunljivi topološki prostori", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:232132

Metadata
TitleIzračunljivi topološki prostori
AuthorMarija Lijović
MentorZvonko Iljazović (mentor)
Committee memberZvonko Iljazović (predsjednik povjerenstva)
Committee memberTina Bosner (član povjerenstva)
Committee memberMatija Kazalicki (član povjerenstva)
Committee memberGoranka Nogo (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj rad podijeljen je na tri glavna poglavlja. Kroz prvo poglavlje navode se osnovni pojmovi izračunljivosti, proučavaju se rekurzivne funkcije \(\mathbb{N}^k \to \mathbb{Z}, \mathbb{N}^k \to \mathbb{Q}\) i \(\mathbb{N}^k \to \mathbb{R}\) te se dokazuju rezultati vezani za te funkcije koji su potrebni u nastavku rada. U drugom poglavlju definiraju se metrički i topološki prostori te se dokazuju određeni rezultati vezani uz pojam neprekidnosti, konvergencije niza, kompaktnosti, Hausdorffovog prostora te uz pojam baze topologije. Treće poglavlje posvećeno je proučavanju izračunljivih topoloških prostora. Uvođenje izračunljivih topoloških prostora motivirano je proučavanjem izračunljivih metričkih prostora te nekih njegovih važnih svojstava.
Abstract (english)
This thesis consists of three main parts. The first part of thesis is devoted to the basic terms of computation, definition of recursive function \(\mathbb{N}^k \to \mathbb{Z}, \mathbb{N}^k \to \mathbb{Q}\) and \(\mathbb{N}^k \to \mathbb{R}\) as well as to some important results regarding these recursive functions. The definitions of metric and topological spaces are presented in the second part of thesis. This part states and discusses the main results related to the continuity, convergence of sequence, compactness, Hausdorff spaces as well as to the notion of a basis for a topology. The third part of thesis is dedicated to the computable topological spaces. Introduction of computable topological spaces was motivated by computable metric spaces and some of its important properties.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:232132
Study programmeTitle: Computer Science and Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra računarstva i matematike (magistar/magistra računarstva i matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-22 12:57:01