20.500.12556/DKUM-45104 Parakompaktni prostori Paracompact spaces V diplomskem delu so obravnavani parakompaktni prostori. To so Hausdorffovi prostori za katere velja, da ima vsako njihovo odprto pokritje finejše lokalno končno odprto pokritje. V prvem delu so opisani osnovni pojmi, ki jih potrebujemo za razumevanje celotnega dela, nato sta opisani lokalna končnost in kompaktnost. V zadnjem poglavju so opisani parakompaktni prostori in njihove lastnosti. Spoznali bomo, kateri prostori so parakompaktni, prav tako bomo spoznali pojem particija enote in jo povezali s pojmom parakompaktnosti. Na koncu se bomo posvetili še nekaterim pokritjem kot sta zvezdno pokritje in baricentrično pokritje, ki pomagata pri prepoznavanju parakompaktnih prostorov. In Graduation Thesis we are dealing with paracompact spaces. These are Hausdorff spaces for which every of their open cover has a locally finite open refinement. In the first part of the thesis we describe the basic concepts that are needed for understanding the subject of the Graduation Thesis. Afterwords, we describe the notion of local finiteness and compactness. In the last chapter we describe paracompact spaces and introduce some of their properties. We also give some caracterisations of paracompact spaces using the notion of partition of unity. At the end, we focus on some other covers such as star covers and barycentric covers which help with caracterising paracompact spaces. kompaktnost parakompaktnost finejše pokritje lokalna končnost compactness paracompactness refinement local finiteness true true false [V. Kračun] Slovenski jezik Angleški jezik Diplomsko delo 2014-08-06 08:30:37 2014-09-25 15:36:52 2022-05-14 03:07:32 2021-04-30 03:15:24 2014 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 515.12(043.2) 20791048 URN:SI:UM:DK:ALTJCLWK UNI_Kracun_Veronika_2014.pdf UNI_Kracun_Veronika_2014.pdf 1 1F122E7785D97452E886B7F361E7956B 829228f78597a5a163866dca02876eb5e484499c6a9a46fcea2f665799fe772a 03faa22f-7c0b-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=65132 Fakulteta za naravoslovje in matematiko 0 0 0