Razširjanje veznih funkcij posplošenih inverznih zaporedij

Domjan, Katarina

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Title:	Razširjanje veznih funkcij posplošenih inverznih zaporedij
Authors:	ID Domjan, Katarina (Author) ID Banič, Iztok (Mentor) More about this mentor...
Files:	MAG_Domjan_Katarina_2020.pdf (478,16 KB) MD5: 0B7D49523519CFD7A0E0021EB17967B0 PID: 20.500.12556/dkum/fe6e7c8f-227a-42d4-b966-9ab406716063
Language:	Slovenian
Work type:	Master's thesis/paper
Typology:	2.09 - Master's Thesis
Organization:	FNM - Faculty of Natural Sciences and Mathematics
Abstract:	V topologiji se je pojavil naslednji odprti problem: Če imamo dano neprazno zaprto podmnožico kartezičnega produkta števno neskončno nepraznih kompaktnih metričnih prostorov, ali sta naslednji trditvi ekvivalentni? 1. Obstajajo zaprti pod prostori zgoraj omenjenih nepraznih kompaktnih metričnih prostorov in navzgor pol zvezne več lične funkcije, ki pripadajo tem zaprtim pod prostorom, tako, da je zgoraj omenjena neprazna zaprta podmnožica kartezičnega produkta inverzna limita posplošenega inverznega zaporedja teh zaprtih pod prostorov in njim pripadajočih navzgor pol zveznih več ličnih funkcij. 2. Obstajajo navzgor pol zvezne več lične funkcije zgoraj omenjenih nepraznih kompaktnih metričnih prostorov tako, da je zgoraj omenjena neprazna zaprta podmnožica kartezičnega produkta inverzna limita posplošenega inverznega zaporedja teh nepraznih kompaktnih metričnih prostorov in njim pripadajočih navzgor pol zveznih funkcij. V uvodnem poglavju magistrskega dela se definirajo osnovni pojmi metričnih prostorov, topoloških prostorov, povezanosti in kompaktnosti le-teh ter kontinuumov. Dokažejo se osnovne lastnosti. V drugem poglavju se spozna pojem inverznih zaporedij in inverznih limit enoličnih ter več ličnih funkcij. V tretjem poglavju se dokažejo glavni rezultati, ki rešijo odprt problem v pozitivno. V četrtem poglavju se spozna krepka in šibka L-razširitvena lastnost posplošenih inverznih zaporedij kot posledica glavnih rezultatov tretjega poglavja in se podrobneje dokaže lastnost krepke in šibke surjektivne razširitvene lastnosti.
Keywords:	Metrični prostor, topološki prostor, kontinuum, kompaktnost, posplošeno inverzno zaporedje, posplošena inverzna limita, razširitvene funkcije, šibka surjektivna razširitvena lastnost, krepka surjektivna razširitvena lastnost.
Place of publishing:	Maribor
Publisher:	[K. Domjan]
Year of publishing:	2020
PID:	20.500.12556/DKUM-76733
UDC:	515.1(043.2)
COBISS.SI-ID:	34654467
NUK URN:	URN:SI:UM:DK:AQRO6LFF
Publication date in DKUM:	29.10.2020
Views:	32127
Downloads:	95
Metadata:
Categories:	FNM
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Licences

License:	CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Link:	http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:	The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:	27.06.2020

Secondary language

Language:	English
Title:	Extending bonding functions in generalized inverse sequences
Abstract:	In topology an open problem was given: Let there be a non-empty closed subset of Cartesian product of countably infinite non-empty compact metric spaces. Are the following statements equivalent? 1. There are closed subspaces of these non-empty compact metric spaces and upper semicontinuous functions for these closed subspaces such that above mentioned non-empty closed subset is the inverse limit of inverse sequence of these closed subspaces and their upper semicontinuous functions. 2. There are upper semicontinuous functions of above mentioned non-empty compact metric spaces such that above mentioned non-empty closed subset is the inverse limit of inverse sequence of these non-empty compact metric spaces and their upper semicontinuous functions. In the introductory chapter basics definitions of metric spaces, topological spaces, connectedness, compactness and continua are given. Basic properties are proven as well. In the second chapter we define the notion of inverse sequences and inverse limits of single-valued and set-valued functions. In the third chapter we proof the main results that give the answer to the above mentioned problem in positive. In the fourth chapter we introduce the notions of strong and weak L-extension property of an inverse sequence as a corollary of main results of chapter three. We also discuss the strong and weak surjective extension properties of an inverse sequence.
Keywords:	Metric space, topological space, continuum, compact, generalized inverse sequence, generalized inverse limit, extending bonding functions, weak surjective extension property, strong surjective extension property.

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