Topološki Radonov izrek : delo diplomskega seminarja

Burger, Evgenija (author), Pavešić, Petar (mentor)

Radonov izrek in njegova topološka posplošitev med sabo povezujeta pojme iz kombinatorike, geometrije, algebre in topologije. Medtem ko lahko Radonov izrek enostavno dokažemo z nekaj linearne algebre, sloni dokaz topološke različice na Borsuk-Ulamovem izreku, ki pa velja za enega pomembnejših eksistenčnih izrekov v topologiji.

• Language: Slovenian
• Keywords: topološki Radonov izrek, Borsuk-Ulamov izrek, Van Kampen-Floresov izrek, simpleks
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-130528
• UDC: 515.1
• COBISS.SI-ID: 77402883
• Publication date in RUL: 16.09.2021

Secondary language

• Language: English
• Title: Topological Radon Theorem

Abstract

Radon's theorem and its topological generalization link together conncepts from combinatorics, geometry, algebra and topology. While Radon's theorem is easy to prove with the help of linear algebra, the proof of topological Radon's theorem requires the use of Borsuk-Ulam theorem, which is an existence theorem with great significance in topology.

• Keywords: topological Radon theorem, Borsuk-Ulam theorem, Van Kampen-Flo-res theorem, simplex