Lindolöfovi prostori

Starc, Vesna

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Title:	Lindolöfovi prostori
Authors:	ID Starc, Vesna (Author) ID Banič, Iztok (Mentor) More about this mentor...
Files:	UNI_Starc_Vesna_2013.pdf (435,58 KB) MD5: B5194BC033C552083240E62D757DC5CA
Language:	Slovenian
Work type:	Undergraduate thesis
Typology:	2.11 - Undergraduate Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	Lindelöfovi prostori so regularni topološki prostori, katerih vsako odprto pokritje vsebuje števno podpokritje. Lindelöfova lastnost je poslošitev bolj znanega pojma kompaktnosti, ki zahteva obstoj končnega podpokritja. V diplomskem delu so zajete lastnosti Lindelöfovih prostorov, opisani so njihovi osnovni primeri in izreki. V prvem delu so navedeni osnovni pojmi, ki jih potrebujemo pri opisovanju Lindelöfovih prostorov. Drugi del obravnava pojem kompaktnosti. V tretjem delu je opisano kaj so Lindelöfovi prostori, njihove lastnosti, primeri in kaj velja za produkt Lindelöfovih prostorov. Na koncu se diplomsko delo dotakne še zgodovine Lindelöfovih prostorov. Končna ugotovitev kaže na to, da določene lastnosti kompaktnih prostorov veljajo tudi za Lindelöfove prostore. Na primer, da je vsak 2-števen prostor Lindelöfov in da je vsak Lindelöfov prostor normalen. Tudi zvezna preslikava ohranja Lindelöfovo lastnost, kar pa ne velja za produkt, saj niti produkt dveh Lindelöfovih prostorov ni nujno Lindelöfov.
Keywords:	Lindelöf, kompaktnost, pokritje, podpokritje
Place of publishing:	Maribor
Publisher:	[V. Starc]
Year of publishing:	2013
PID:	20.500.12556/DKUM-43239
UDC:	515.122(043.2)
COBISS.SI-ID:	20315912
NUK URN:	URN:SI:UM:DK:PJ06DVVT
Publication date in DKUM:	30.01.2014
Views:	1637
Downloads:	100
Metadata:
Categories:	FNM
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Secondary language

Language:	English
Title:	Lindelöf spaces
Abstract:	Lindelöf spaces are regular topological spaces such that each of their open covers contains a countable subcover. The Lindelöf spaces are a generalization of the notion of compact spaces, which require the existence of a finite subcover. In the Graduation Thesis, the basic properties of Lindelöf spaces are given. We also produce many useful examples. In the first part of the thesis, we introduce the basic concepts that are needed to describe the Lindelöf spaces. In the second part we discuss the notion of compactness, and, finally in the third part, we introduce the Lindelöf spaces, describe many of their properties, and produce many examples. We also give a special emphasis to the product of the Lindelöf spaces. At the end of the thesis we give a historic overview on the Lindelöf spaces. As a final finding we may conclude that certain properties of compact spaces also apply to the Lindelöf spaces; for example, every second-countable space is a Lindelöf space and every Lindelöf space is normal. Even more, every continuous map is the Lindelöf property preserving map. However, the product of two Lindelöf spaces is not necessarily a Lindelöf space.
Keywords:	Lindelöf, compactness, cover, subcover

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