doktorska disertacija
Matej Merhar (Author), Iztok Banič (Mentor), Uroš Milutinović (Co-mentor)

Abstract

V doktorski disertaciji se obravnava vprašanje ali iz konvergence grafov navzgor polzveznih veznih funkcij sledi konvergenca ustreznih pripadajočih inverznih limit za konstantna inverzna zaporedja kompaktnih metričnih prostorov. V uvodnem delu se vpeljejo osnovni pojmi kot so navzgor polzvezne funkcije, inverzna zaporedja in inverzne limite. V osrednjem delu se na konkretnih primerih pokaže, da je odgovor na zgoraj zastavljeno vprašanje v splošnem negativen in v obliki izrekov poda dodatne pogoje za vezne funkcije, ki zagotavljajo, da iz konvergence njihovih grafov sledi konvergenca pripadajočih inverznih limit. Med drugim se dokaže, da če so vezne funkcije surjektivne in funkcija h kateri njihovi grafi konvergirajo enolična, tedaj tudi zaporedje pripadajočih inverznih limit konvergira. Te pogoje se v nadaljevanju nekoliko omili in posploši na splošna inverzna zaporedja. Predstavi se tudi uporaba navedenih rezultatov za konstrukcijo poti v hiperprostorih. V zaključnem poglavju se navede še nekatera odprta vprašanja, ki odpirajo možnost nadaljnjega raziskovanja.

Keywords

kontinuum;hiperprostor;limita;inverzna limita;preslikave;pot;disertacije;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: M. Merhar]
UDC: 515.126(043.3)
COBISS: 269163264 Link will open in a new window
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Other data

Secondary language: English
Secondary title: Limits of inverse limits
Secondary abstract: In the thesis the following question is considered. Given a constant inverse sequences with compact metric spaces and upper semi-continuous set-valued functions is it true that if the graphs of the these functions converge, then so do the corresponding inverse limits? In the first part of the thesis basic definitions and notations are given such as upper semi-continuous functions, sequences and inverse limits. It is shown that in general the answer to the above question is negative and proved in forms of theorems that under certain conditions for the bonding functions the convergence of the corresponding inverse limits follows from the convergence of the graphs of the bonding functions. Among other results it is shown that if the bonding functions are surjective and the function they converge to is single valued, then the convergence of the graphs of the bonding functions implies the convergence of the corresponding inverse limits. These conditions are then replaced by certain milder conditions and generalized to non-constant inverse sequences. Also an application of the above results for the construction of paths in hyperspaces is provided. The thesis is concluded by some open questions that give the possibility of further research.
Secondary keywords: continua;hyperspace;limit;inverse limit;function;path;dissertations;
URN: URN:SI:UM:
Type (COBISS): Doctoral dissertation
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: VII, 65 str.
ID: 8727865