Elementarni aspekti diferencijalne topologije

master's thesis

• Title (english): Elementary aspects of differential topology
• Author: Matko Brandić Lipinski
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Zlatko Drmač (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Committee member: Slaven Kožić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-03-05, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Kako bismo čitatelju dovoljno dobro približili diferencijalnu topologiju, najprije navodimo neke elementarne (i manje elementarne) pojmove i rezultate metričkih prostora, topologije i diferencijalnog računa kako bismo čitatelja istovremeno upoznali sa simbolikom koja će se koristiti kroz rad, te spomenuli i/ili podsjetili na svojstva koja će nam u kasnijim koracima biti od koristi. U drugom dijelu upoznajemo čitatelja s homeomorfzmom i difeomorfzmom te na bitnom primjeru pokazujemo glavnu razliku između ta dva pojma. Za kraj, spomenut ćemo neke osnovne rezultate vezane uz mnogostrukosti.

Abstract (english)

In order to familiarize the reader with differential topology, we will first state some elementary (and less elementary) terminology and results from metric spaces, topology and calculus in order to simultaneously introduce the symbolism which will be used throughout the thesis and to mention and/or remind of the properties which will be needed in later steps. In the second part, we will introduce homeomorphism and difeomorphism, and we will show the main difference between these two terms in a very important example. Finally, we will mention some basic results concerning manifolds.

• Keywords: metrički prostor; topologija; diferencijalni račun; homeomorfzam; difeomorfzam
• Keywords (english): metric spaces; topology; calculus; homeomorphism; difeomorphism
• Language: croatian
• URN:NBN: urn:nbn:hr:217:041200
• Study programme: Title: Applied Mathematics; 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: 2021-03-23 11:43:23