Kvocijentni prostori

master's thesis

• Author: Lovro Švenda
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Siniša Slijepčević (član povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-25, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U radu su istražena svojstva topoloških prostora kojima je topologija inducirana kvocijentnim preslikavanjem. Ispitani su dovoljni uvjeti (korolar 2.3.21) na prostore \(X\) i \(Y\) te funkciju \(f : X \to Y\) da inducirano preslikavanje \(\bar{f}\) bude homeomorfizam. Na primjeru kružnice uočeno je da kvocijentna topologija \(\mathcal{F}\) ukazuje na izbor točaka koje se identificiraju ili "spajaju". Ostali primjeri (Möbiusova vrpca, torus i Kleinova boca) su konstruirani direktno, zadavanjem kvocijentne topologije.

Abstract (english)

This paper investigates the properties of topological spaces where the topology is induced by a quotient map. Sufficient conditions on spaces \(X\) and \(Y\) and a map \(f : X \to Y\) so that the induced map \(\bar{f}\) is a homeomorphism are found. (Corollary 2.3.21). The example with a circle shows that quotient topology \(\mathcal{F}\) indicates the choice of the points to be identified or "glued" together. Other examples (Möbius strip, torus and Klein bottle) are constructed directly, by giving the quotient topology.

• Keywords: topološki prostori; kvocijentna topologija; topologija inducirana kvocijentnim preslikavanjem; inducirano preslikavanje; homeomorfizam
• Keywords (english): topological spaces; quotient topology; topology induced by a quotient map; induced map; homeomorphism
• Language: croatian
• URN:NBN: urn:nbn:hr:217:556810
• 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: 2019-02-15 07:56:33