Lokalna izračunljivost

master's thesis

• Author: Igor Sušić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Committee member: Boris Muha (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

Ukratko, rad je logički podijeljen u tri poglavlja. U prvom poglavlju govorimo općenito o izračunljivosti. U drugom poglavlju govorimo o izračunljivim metričkim prostorima. Nadalje, govorimo o rekurzivnim brojevima, gustim nizovima, rekurzivno prebrojivim skupovima, poluizračunljivim skupovima i navodimo mnoge rezultate iz teorije metričkih prostora s ciljem povezivanja sa teorijom izračunljivosti. U trećem poglavlju poopćavamo neke rezultate za izračunljive metričke prostore na izračunljive topološke prostore.

Abstract (english)

This paper is logically divided into three chapters. In the first chapter, we talk generally about computability. In the second chapter, we talk about computable metric spaces. Furthermore, we talk about recursive numbers, dense sequences, recursively enumerable sets, semi-computable sets and we state many results from the theory of metric spaces in order to establish some connections with the theory of computability. In the third chapter, we generalize some results for computable metric spaces to computable topological spaces.

• Keywords: izračunljivi metrički prostori; rekurzivni brojevi; gusti nizovi; rekurzivno prebrojivi skupovi; poluizračunljivi skupovi; izračunljivi topološki prostori
• Keywords (english): computable metric spaces; recursive numbers; dense sequences; recursively enumerable sets; semi-computable sets; computable topological spaces
• Language: croatian
• URN:NBN: urn:nbn:hr:217:144123
• Study programme: Title: 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 resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-08 10:55:20