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Title:ODPRTE PRESLIKAVE UVERIŽLJIVIH KONTINUUMOV
Authors:Skornšek, Sabina (Author)
Banič, Iztok (Mentor) More about this mentor... New window
Files:.pdf UNI_Skornsek_Sabina_2012.pdf (913,27 KB)
 
Language:Slovenian
Work type:Undergraduate thesis (m5)
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:V diplomskem delu bomo v uvodnem poglavju skupaj s primeri predstavili osnovne pojme v topologiji, povezane in kompaktne prostore. V drugem poglavju bomo definirali kontinuume in si pogledali nekaj osnovnih primerov. Del poglavja je namenjen uverižljivim kontinuumom, kjer bomo definirali nekaj lastnosti le-teh. V tretjem poglavju se bomo seznanili z odprtimi preslikavami v povezavi z uverižljivimi kontinuumi. Dokazali bomo pomemben izrek, ki pravi, da je slika vsakega uverižljivega kontinuuma z odprto preslikavo spet uverižljiv kontinuum. Zanimiva teorija se razvije v četrtem poglavju v povezavi z lokalnimi homeomorfizmi. Dokazali bomo, da če je preslikava iz uverižljivega kontinuuma na nek prostor lokalni homeomorfizem, potem je homeomorfizem. Omenjena dokaza iz tretjega in četrtega poglavja pa sta tudi najpomembnejša rezultata diplomskega dela.
Keywords:kontinuum, uveržljiv kontinuum, odprta preslikava, lokalni homeomorfizem
Year of publishing:2012
Publisher:[S. Skornšek]
Source:Maribor
UDC:51(043.2)
COBISS_ID:19364616 Link is opened in a new window
NUK URN:URN:SI:UM:DK:GLESCCYT
Views:933
Downloads:81
Metadata:XML RDF-CHPDL DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:OPEN MAPS OF CHAINABLE CONTINUA
Abstract:In introductory chapter of graduation thesis we introduce basic concepts of topology, connected spaces and compact spaces with basic examples. In second part of graduation thesis we define the concept of continuum with examples. The second part of the section is dedicated to chainable continua, where some characteristics of them are presented. In the third section we introduce open maps and their relations to chainable continua. We prove important theorem which says that image of a chainable continuum with open map is a chainable continuum. An interesting theory is developed in fourth section describing results of local homeomor- phism. We prove that a local homeomorphism of chainable continua onto another space is actually a homeomorphism. Mentioned results from the third and the fourth section are the most important results of graduation thesis.
Keywords:continuum, chainable continuum, open map, local homeomorphism


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