20.500.12556/DKUM-62612 Hahn-Mazurkiewiczev izrek The Hahn-Mazurkiewicz theorem Diplomsko delo obravnava Peanove kontinuume in njihove lastnosti, ter Hahn-Mazurkiewiczev izrek. V prvem delu bomo definirali pojme in dokazali izreke, ki so bistvenega pomena za razumevanje Hahn-Mazurkiewiczevega izreka. Pri tem bo poseben poudarek na lokalni povezanosti prostora in primerih le teh. Osrednji del se bo začel z definicijo Peanovega prostora in lastnosti S. Zaključili bomo z Hahn-Mazurkiewiczevim izrekom in bomo s tem dokazali, da je vsak lokalno povezani kontinuum zvezna slika intervala [0,1]. In this graduation thesis we will be looking at Peano continua, their caracteristics and the Hahn-Mazurkiewich theorem. The first chapter will contain definitions and theorems that are crucial to understanding the Hahn-Mazurkiewicz theorem. There will be a special weight on local connectivity of spaces and examples of these. The central part will begin with the definition of Peano space and property S. We will end with proof of the Hahn-Mazurkiewicz theorem and thus prove that each locally connected continuum is a continuus image of the closed interval [0,1]. lokalna povezanost šibke verige lastnost S local conectivity weak chain property S true true false [K. Erhatič] Slovenski jezik Angleški jezik Diplomsko delo 2016-08-30 07:40:50 2016-09-27 16:16:47 2022-06-29 03:09:20 2019-07-11 13:01:32 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.127(043.2) 22583816 URN:SI:UM:DK:U4HKHGUA UN_Erhatic_Karmen_2016.pdf UN_Erhatic_Karmen_2016.pdf 1 4A324A28C2386BFDDB54A4258BF17060 ffb0a61bd062dc08a98f73e894ccda28ba792576ea3ed427d64206187d1eb9fc 3034c4c9-7c0d-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=100949 Fakulteta za naravoslovje in matematiko 0 0 0