20.500.12556/DKUM-37987 ODPRTE PRESLIKAVE UVERIŽLJIVIH KONTINUUMOV OPEN MAPS OF CHAINABLE CONTINUA 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. 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. kontinuum uveržljiv kontinuum odprta preslikava lokalni homeomorfizem continuum chainable continuum open map local homeomorphism true true false [S. Skornšek] Slovenski jezik Angleški jezik Diplomsko delo 2012-09-14 08:53:11 2012-10-08 11:50:26 2022-04-25 23:04:44 2021-04-19 03:21:00 2012 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 19364616 URN:SI:UM:DK:GLESCCYT UNI_Skornsek_Sabina_2012.pdf UNI_Skornsek_Sabina_2012.pdf 1 CCACF2825C6C139E23A54C1518ADFDF7 dd717954d58ac9c99d9750f0e813ea4717570797c0e3b6f82a0186687b9160f5 62565c3e-7c08-11eb-bb7a-00155d0001ca 20.500.12556/dkum/6b6ce1f1-8a4b-490a-abbf-6319f4e0f590 https://dk.um.si/Dokument.php?lang=slv&id=50398 Fakulteta za naravoslovje in matematiko 0 0 0