Lančasti kontinuumi

master's thesis

• Author: Marina Čičak
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Maja Starčević (član povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Committee member: Sonja Štimac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavaju se lančasti kontinuumi. Rad je podijeljen na četiri poglavlja. U prvom poglavlju upoznajemo se s metričkim i topološkim prostorima te njihovim svojstvima, sličnostima i razlikama. U drugom poglavlju proučavamo pojam otvorenog pokrivača te svojstva kompaktnosti, posebno u metričkim prostorima, a zatim u euklidskom prostoru. U trećem poglavlju definiramo pojam povezanog topološkog prostora, a u četvrtom definiramo lančaste kontinuume te proučavamo njihova svojstva.

Abstract (english)

In this thesis we examine chainable continua. This thesis is divided four chapters. In the first chapter we introduce metric and topological spaces and we study their properties, their similarities and differences. In the second chapter we examine the notion of an open cover and properties of compactness, in particular in metric spaces and in Euclidean space. In the third chapter we define the notion of a connected topological space and in fourth chapter we define chainable continua and we study their properties.

• Keywords: metrički prostori; topološki prostori; otvoreni pokrivač; euklidski prostor
• Keywords (english): metric spaces; topological spaces; open cover; Euclidean space
• Language: croatian
• URN:NBN: urn:nbn:hr:217:124620
• 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: Access restricted to students and staff of home institution
• Created on: 2019-01-07 13:12:29