Poluizračunljivost

master's thesis

• Author: Eugen Čičković
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Mladen Vuković (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Committee member: Ante Mimica (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu smo uveli pojam rekurzivne funkcije i to kada je kodomena skup prirodnih, cijelih, racionalnih i realnih brojeva. Promatrali smo svojstva istih i primijenili ih u sklopu metričkih i topoloških prostora te došli do definicije izračunljivog metričkog i izračunljivog topološkog prostora. U trećem dijelu rada smo se bazirali na definiranju i svojstvima izračunljivih i poluizračunljivih skupova te smo zaključno odredili dovoljne uvjete da za neki skup možemo reći da je izračunljiv.

Abstract (english)

In this thesis we introduced the notion of a recursive function in case when the codomain is the set of natural numbers, integers, rational and real numbers. We examined properties of these functions and we applied them in the context of metric and topological spaces. We defined computable metric spaces and computable topological spaces. In the third part of the thesis we defined and studied properties of computable and semi-computable sets and we found sufficient conditions for some set to be computable.

• Keywords: rekurzivna funkcija; izračunljivi metrički prostor; izračunljivi topološki prostor; izračunljivi skupovi; poluizračunljivi skupovi
• Keywords (english): recursive function; computable metric space; computable topological space; computable sets; semi-computable sets
• Language: croatian
• URN:NBN: urn:nbn:hr:217:207002
• Study programme: Title: Mathematics and Computer Science Education; specializations in: Mathematics and Computer Science Education; Course: Mathematics and Computer Science Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike i informatike (magistar/magistra edukacije matematike i informatike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-07 13:28:22