Disperzija i potpuna omeđenost

master's thesis

• Author: Tamara Bilić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Tina Bosner (član povjerenstva)
• Committee member: Matija Kazalicki (član povjerenstva)
• Committee member: Robert Manger (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj diplomski rad je podijeljen na tri poglavlja. U prvom poglavlju proučavali smo omeđenost i potpunu omeđenost u metričkim prostorima. U drugom poglavlju bavili smo se disperzijom u metričkim prostorima te posebno r-gustim konačnim nizovima, r-raspršenim konačnim nizovima i maksimalnom raspršenošću. U trećem poglavlju proučavali smo pojam n-kapaciteta skupa u metričkom prostoru. Naveli smo neke primjere s tim u vezi te smo se bavili odnosom aproksimacije skupa i kapaciteta.

Abstract (english)

This diploma thesis is divided into three chapters. In the first chapter we studied boundedness and completed boundedness in metric spaces. In the second chapter we examined dispersion in metric spaces and in particular we examined r-dense finite sequences, r-dispersed finite sequences and maximal dispersion. In the third chapter we studied the notion of n-capacity of a set in a metric space. We gave some examples and we examined the relationship between an approximation of a set and capacity.

• Keywords: disperzija; omeđenost; potpuna omeđenost; metrički prostori; konačni nizovi
• Keywords (english): dispersion; boundedness; completed boundedness; metric spaces; finite sequences
• Language: croatian
• URN:NBN: urn:nbn:hr:217:451526
• 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: 2017-05-25 11:54:54