Posplošeni Brouwerjev izrek : delo diplomskega seminarja

Žajdela, Gašper (author), Vavpetič, Aleš (mentor)

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.

• Language: Slovenian
• Keywords: retrakcija, negibna točka, simpleks, simplicialni kompleks
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-126993
• UDC: 515.1
• COBISS.SI-ID: 69461507
• Publication date in RUL: 12.05.2021

Secondary language

• Language: English
• Title: Generalized Brouwer theorem

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.

• Keywords: retraction, fixed point, simplex, simplicial complex