Hindmanov teorem

master's thesis

• Title (english): Hindman's theorem
• Author: Božidar Grgur Drmić
• Mentor: Mladen Vuković (mentor)
• Committee member: Mladen Vuković (predsjednik povjerenstva)
• Committee member: Vedran Čačić (član povjerenstva)
• Committee member: Marko Horvat (član povjerenstva)
• Committee member: Zvonko Iljazović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2022-07-20, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Centralni dio ovoga rada dokaz je Hindmanovog teorema upotrebom strukture ultrafiltera. Za potrebe toga definiraju se pojmovi filtra i ultrafiltra te se navode primjeri i dokazuju neka njihova svojstva potrebna za dokaz Hindmanovog teorema. Također se uvode neki pojmovi iz topologije i dokazuju osnovni teoremi. Na samom kraju rada bez dokaza je navedeno nekoliko poopćenja i analogona Hindmanovog teorema.

Abstract (english)

Focus of this thesis is on proving the Hindman’s Theorem by utilising the structure of ultrafilters. Therefore, we define the concepts of filters and ultrafilters with examples and prove some of their properties required in order to prove Hindman’s Theorem. We also introduce some of the concepts from topology and prove some basic results. At the very end, we have listed some of the generalisations and analogous results of Hindman’s Theorem.

• Keywords: filtar; struktura ultrafiltera; topologija
• Keywords (english): filters; structure of ultrafilters; topology
• Language: croatian
• URN:NBN: urn:nbn:hr:217:222243
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-09-13 09:11:15