Izrek Monskega : delo diplomskega seminarja

Megušar, Vid (author), Strle, Sašo (mentor)

Glavni cilj diplomskega dela je dokaz izreka Monskega. Pomembni orodji za dokaz izreka sta Spernerjeva lema in p-adična norma. V delu zato predstavimo in dokažemo Spernerjevo lemo. p-adično normo definiramo na polju racionalnih števil in pokažemo, da jo je mogoče razširiti na realna števila.

• Language: Slovenian
• Keywords: Spernerjeva lema, p-adična norma, razširitev polja
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-117823
• UDC: 512
• COBISS.SI-ID: 58416131
• Publication date in RUL: 29.07.2020

Secondary language

• Language: English
• Title: Monsky's Theorem

Abstract

The main goal of this work is to present a proof of Monsky's Theorem. Two of the important tools to prove the theorem are Sperner's lemma and p-adic norm. In the work we formulate and prove Sperner's lemma. We define p-adic norm on the field of rational numbers and show that it is possible to extend it to the field of real numbers.

• Keywords: Sperner's lemma, p-adic norm, field extension