Posplošeni Brouwerjev izrek

delo diplomskega seminarja

Gašper Žajdela (Author), Aleš Vavpetič (Mentor)

Abstract

V diplomskem delu na kratko predstavimo Brouwerjev izrek o negibni točki in izrek o neobstoju retrakcije. Izkaže se, da sta izreka ekvivalentna, kar v delu tudi dokažemo. Predstavimo osnove simpleksov in simplicialnih kompleksov. Na koncu dela posplošimo izrek o neobstoju retrakcije na razred kompaktnih dvodimenzionalnih poliedrov. Delo zaključimo z zgledom, ki pokaže, da ekvivalenca prej omenjenih izrekov pri naši posplošitvi ne velja.

Keywords

matematika;retrakcija;negibne točke;simpleks;simplicialni kompleks;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[G. Žajdela]
UDC:	515.1
COBISS:	69461507
Views:	1292
Downloads:	121
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Generalized Brouwer theorem
Secondary abstract:	In this thesis, we briefly present Brouwer fixed point theorem and the no retraction theorem. It turns out that the theorems are equivalent, which we also prove in this thesis. We present the basics of simplices and simplicial complexes. At the end of this thesis, we generalize the no retraction theorem to a broad class of compact 2-dimensional polyhedra. We conclude with an example that shows that the equivalence of the aforementioned theorems in general does not hold.
Secondary keywords:	mathematics;retraction;fixed point;simplex;simplicial complex;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	29 str.
ID:	12887513