Uniformna metrika

master's thesis

• Author: Lucija Borovec
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Committee member: Filip Najman (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-09-24, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U prvom poglavlju se definiraju metrika i metrički prostori. Proučavaju se otvoreni, zatvoreni i omeđeni skupovi u metričkom prostoru. Specijalno se promatraju neprekidne funkcije u metričkom prostoru te povezanost neprekidnih funkcija i konvergencije. U drugom poglavlju se upoznajemo sa osnovnim pojmovima iz topologije. Definira se topološki prostor, potprostor topološkog prostora i baza topologije. I ovdje se najviše proučavaju neprekidne funkcije. Treće poglavlje je posvećeno kompaktnosti i uniformnoj metrici. Definira se uniformna metrika te kompaktni metrički i topološki prostor. Osobito se proučava uniformna konvergencija. Ovo poglavlje ujedno prikazuje povezanost metričkih i pripadnih topoloških prostora.

Abstract (english)

The first chapter defines the metric and metric spaces. Open, closed and bounded sets in a metric space are studied here. Continuous functions in a metric space and convergent sequences in a metric space are especially observed. The second chapter is an introduction to the basic concepts of topology. We define the topological space, subspace of an topological space and the base of topology. Even here are continuous function and convergent sequences specially observed. The third chapter is devoted to compactness and uniform metrics. We define the uniform metric and compact metric and topological spaces. Special emphasis is on the study of uniform convergence. This section also shows the connection between metric and associated topological spaces.

• Keywords: metrika; metrički prostor; neprekidne funkcije; topološki prostor; kompaktnost; uniformna metrika; kompaktni metrički prostor; kompaktni topološki prostor; uniformna konvergencija
• Keywords (english): metric; metric space; continuous functions; topological space; compactness; uniform metrics; compact metric space; compact topological space; uniform convergence
• Language: croatian
• URN:NBN: urn:nbn:hr:217:788973
• 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: 2017-06-07 11:43:41