Dekompozicije kontinuumov

diplomsko delo

Barbara Veit (Author), Iztok Banič (Mentor)

Abstract

V diplomskem delu bomo v uvodnem poglavju predstavili osnovne pojme in osnovne primere kontinuumov. Pogledali bomo eno izmed najpomembnejših tehnik za pridobivanje novih kontinuumov, to je tehnika vgnezdenih presekov, in na koncu pogledali še nekaj kontinuumov, ki so pridobljeni s to tehniko. V drugem poglavju bomo dokazali Urysohnovo lemo in na koncu še Urysohnov metrizabilnostni izrek, ki bo ključen pri dokazih v naslednjem poglavju. V zadnjem poglavju diplomskega dela se bomo seznanili s pojmoma dekompozicijski prostor in dekompozicijska topologija. Definirali bomo navzgor pol zvezne dekompozicije, ki jih bomo kasneje uporabili pri konstruiranju novih zanimivih kontinuumov.

Keywords

matematika;kontinuumi;preseki;dekompozicija;prostori;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[B. Veit]
UDC:	51(043.2)
COBISS:	18485768
Views:	1635
Downloads:	85
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	DECOMPOSITIONS OF CONTINUA
Secondary abstract:	In introductory chapter of graduation thesis we introduce basic concepts and basic examples of continua. We define one of the most important technique for constructing new continua, called nested intersections. At the end we give some examples of continua which are constructed with these technique. In second part of graduation thesis we prove Urysohn's lemma and also Urysohn's metrization theorem, which is used in proofs in next chapter. At the end of graduation thesis we introduce decomposition space and decomposition topology. We define upper semi-continuous decompositions and give some examples of how upper semi-continuos decompositions can result in interesting continua.
Secondary keywords:	Continua;Nested intersections;Urysohn's lemma;Urysohn's metrization theorem;Decomposition space;Upper semi-continuous decomposition;
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, 42 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19341