Hausdorffova metrika

master's thesis

• Author: Marina Volarić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Marko Vrdoljak (član povjerenstva)
• Committee member: Miljenko Marušić (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

Tema ovog diplomskog rada je Hausdorffova metrika. U prvom poglavlju se definira pojam metričkoga prostora te se također definiraju neki pojmovi s tim u vezi. U drugom poglavlju se definira Hausdorffova udaljenost između dva skupa. Nadalje, promatraju se pseudometrika, zatvoreni skupovi, potpuno omeđeni skupovi, gusti skupovi te pojam zatvarača skupa te se ispituju veze ovih pojmova i Hausdorffove udaljenosti.

Abstract (english)

The subject of this thesis is Hausdorff metric. The first chapter we define the notion of a metric space and we also define some basic notions related to metric spaces. In the second chapter we define the Hausdorff distance between two sets. Furthermore, we observe pseudometric, closed sets, totally bounded sets, dense sets and the notion of the closure of a set and we examine relationships between these notions and the Hausdorff distance.

• Keywords: Hausdorffova metrika; Hausdorffova udaljenost; pseudometrika; zatvoreni skupovi; potpuno omeđeni skupovi; gusti skupovi; zatvarač skupa
• Keywords (english): Hausdorff metric; Hausdorff distance; pseudometric; closed sets; totally bounded sets; dense sets; closure of a set
• Language: croatian
• URN:NBN: urn:nbn:hr:217:792902
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-19 15:09:57