Parakompaktni prostori

diplomsko delo

Veronika Kračun (Author), Iztok Banič (Mentor)

Abstract

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.

Keywords

diplomska dela;topologija;kompaktnost;parakompaktnost;finejše pokritje;lokalna končnost;

Data

Language:	Slovenian
Year of publishing:	2014
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[V. Kračun]
UDC:	515.12(043.2)
COBISS:	20791048
Views:	952
Downloads:	64
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Paracompact spaces
Secondary abstract:	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.
Secondary keywords:	compactness;paracompactness;refinement;local finiteness;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 36 f.
ID:	8729009