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Title:
Limite inverznih limit
Authors:
ID
Merhar, Matej
(Author)
ID
Banič, Iztok
(Mentor)
More about this mentor...
ID
Milutinović, Uroš
(Comentor)
Files:
DR_Merhar_Matej_2013.pdf
(305,50 KB)
MD5: 14EDE63F7A59400337625D5F1565BDA5
Language:
Slovenian
Work type:
Dissertation
Typology:
2.08 - Doctoral Dissertation
Organization:
FNM - Faculty of Natural Sciences and Mathematics
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
,
zvezna preslikava
,
navzgor polzvezna preslikava
,
pot
Place of publishing:
[S. l.
Publisher:
M. Merhar]
Year of publishing:
2013
PID:
20.500.12556/DKUM-42550
UDC:
515.126(043.4)
COBISS.SI-ID:
269163264
NUK URN:
URN:SI:UM:DK:NNUIEWPH
Publication date in DKUM:
08.10.2013
Views:
2530
Downloads:
132
Metadata:
Categories:
FNM
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:
MERHAR, Matej, 2013,
Limite inverznih limit
[online]. Doctoral dissertation. S. l. : M. Merhar. [Accessed 22 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=42550
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Secondary language
Language:
English
Title:
Limits of inverse limits
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.
Keywords:
continua
,
hyperspace
,
limit
,
invers limit
,
continuous function
,
upper semi-continuous function
,
path
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