Cantorov skup

master's thesis

• Author: Magdalena Bašić
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Pavle Pandžić (član povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu proučavali smo Cantorov skup i Cantorov prostor i neka njihova zanimljiva svojstva. Definirali smo neke pojmove u metričkim i topološkim prostorima, kao što su povezanost, kompaktnost, separirani skupovi, totalna nepovezanost, Hausdorffovi i normalni prostori, te dokazali neke tvrdnje s njima u vezi. Posebno smo se koncentrirali na totalno nepovezane kompaktne prostore, kakav je i Cantorov prostor.

Abstract (english)

In this thesis we have studied the Cantor set and the Cantor space and some of their interesting properties. We have defined some notions in metric and topological spaces, such as connectedness, compactness, separated sets, total disconnectedness, Hausdorff and normal spaces, and proved some facts related to them. In particular, we have concentrated on totally disconnected compact spaces, an example of which is the Cantor space.

• Keywords: Cantorov skup; Cantorov prostor; Hausdorffovi prostori
• Keywords (english): Cantor set; Cantor space; Hausdorff spaces
• Language: croatian
• URN:NBN: urn:nbn:hr:217:693466
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-05-23 10:18:59