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1.
GLADKI KONTINUUMI
Tina Sovič, 2009, undergraduate thesis

Abstract: Najprej se bomo seznanili z definicijo kontinuumov. Ogledali si bomo nekaj osnovnih primerov in lastnosti kontinuumov, kot sta ireducibilnost in dedna unikoherentnost. Sledi vpeljava gladkih kontinuumov, nekaj zgledov in njihova splošnejša definicija. Ogledali si bomo njihovo karakterizacijo in navedli nekaj rezultatov v povezavi z dedno unikoherentnostjo. Ob koncu bomo več pozornosti posvetili še ireducibilnim gladkim kontinuumom.
Keywords: Kontinuum, Gladek kontinuum, Dedno unikoherenten kontinuum, Ireducibilnost
Published: 06.07.2009; Views: 1873; Downloads: 170
.pdf Full text (391,67 KB)

2.
Two constructions of continua: inverse limits and compactifications
Tina Sovič, 2013, doctoral dissertation

Abstract: In the thesis we talk about two different constructions of continua. First we present the generalized inverse limits, with help of which we construct Wazewski's universal dendrite. What follows is a description of the compactifications of a ray and the presentation of results about their span. The first chapter will be an introduction to the continuum theory trough interesting examples, as sin(1/x)-continuum, Hilbert cube, Brouwer-Janiszewski-Knaster continuum and pseudoarc. We will present some of their properties, among which irreducibility, smoothness and span zero are the most important ones for us. In the continuation we intend to present some various constructions of continua. The main focus will be on the generalized inverse limits and compactifications of rays, which will also be a central part of the thesis. In this chapter, we also study inverse limits in the category of compact Hausdorff spaces with upper semi-continuous functions. We show that the inverse limits with upper semi-continuous bonding functions, together with the projections are weak inverse limits in this category. The following two are the most important chapters in the thesis. The first is a detailed description of a construction of the family of upper semi-continuous functions f, such that the inverse limit of the inverse sequence of unit intervals and f, as the only bonding function, is homeomorphic to Wazewski's universal dendrite for each of it. Among other results we will also give a complete characterization of comb-functions, for which the inverse limits of the type described above are dendrites. The next important chapter will be about compactifications of rays. In the first part of this chapter we will use compactifications to prove that for each continuum Y there is an irreducible smooth continuum that contains a topological copy of Y. The second part presents the main results of this chapter; i.e. the span of a compactification of a ray with a remainder that has a span zero is also zero. In the proofs of this chapter we will help ourselves with a discretization of span.
Keywords: continua, inverse limit, inverse sequence, upper semi-continuous function, set-valued functions, bonding function, hyperspace, dendrite, universal dendrite, category, compactification, compactification of a ray, smooth continua, irreducible continua, span, span zero
Published: 25.09.2013; Views: 1461; Downloads: 98
.pdf Full text (861,84 KB)

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Ważewski's universal dendrite as an inverse limit with one set-valued bonding function
Iztok Banič, Matevž Črepnjak, Matej Merhar, Uroš Milutinović, Tina Sovič, 2012, original scientific article

Abstract: Konstruirana je družina navzgor polzveznih večličnih funkcij ▫$f:[0,1] rightarrow 2^{[0,1]}$▫, za katere velja, da je inverzna limita inverznega zaporedja intervalov ▫$[0,1]$▫ in ▫$f$▫ kot edine vezne preslikave homeomorfna univerzalnemu dendritu Ważevskega.
Keywords: topologija, kontinuum, inverzna limita, večlična funkcija, dendrit, univerzalni dendrit Ważevskega, topology, continua, inverse limits, upper semi-continuous functions, dendrites, Ważewski's universal dendrite
Published: 10.07.2015; Views: 521; Downloads: 116
URL Link to full text

7.
Inverse limits in the category of compact Hausdorff spaces and upper semicontinuous functions
Iztok Banič, Tina Sovič, 2013, original scientific article

Abstract: V članku obravnavamo inverzne limite v kategoriji ▫$mathcal{CHU}$▫ kompaktnih Hausdorffovih prostorov in navzgor polzveznih (u.s.c) preslikav. Vpeljemo pojem šibkih inverznih limit in pokažemo, da inverzne limite z navzgor polzveznimi veznimi preslikavami skupaj s projekcijami niso nujno inverzne limite v ▫$mathcal{CHU}$▫, so pa vedno šibke inverzne limite v tej kategoriji. Med drugim gre za realizacijo kategorijalnega pristopa k reševanju problema, ki ga je zastavil W. T. Ingram.
Keywords: topologija, kategorije, navzgor polzvezne funkcije, inverzne limite, posplošene inverzne limite, šibke inverzne limite, topology, upper semi-continuous functions, inverse limits, generalized inverse limits, weak inverse limits
Published: 10.07.2015; Views: 410; Downloads: 66
URL Link to full text

8.
Razvoj transporta, logistike in mobilnosti v Sloveniji
Josip Orbanić, Bojan Rosi, 2016, scientific monograph

Published: 26.05.2017; Views: 1392; Downloads: 293
.pdf Full text (11,95 MB)

9.
Matematika 1
Tina Sovič, Simon Špacapan, 2018, reviewed university, higher education or higher vocational education textbook

Abstract: Skripta Matematika 1 zajema osnovna znanja matematike, ki ga potrebujejo študentje visokošolskih programov Fakultete za gradbeništvo,prometno inženirstvo in arhitekturo. V prvem delu skripte so predstavljena poglavja iz področja analize, v drugem delu pa poglavja iz področja algebre. Natančneje, začnemo z zaporedji, kjer opredelimo osnovne pojme, kot so omejenost, monotonost in konvergenca zaporedja. Sledi poglavje, ki na kratko predstavi kompleksna števila in operacije med njimi. Nato so opisane osnovne elementarne funkcije ter predstavljena pojma limita funkcije in zveznost. Definiramo odvod funkcije in pokažemo njegovo uporabo pri določanju lokalnih ekstremov. Odvodu sledi definicija integrala skupaj z njegovo uporabo. Prvi del skripte zaključuje poglavje o funkcijah dveh spremenljivk. V drugem delu predstavimo geometrijske vektorje in operacije med njimi. V nadaljevanju obravnavamo premice in ravnine v prostoru. Skripto zaključimo s poglavjem o matrikah, kjer opišemo osnovne matrične operacije, sisteme enačb in matriko linearne preslikave.
Keywords: zaporedja, funkcije, odvod, integral, vektorji, sistemi enačb, matrike
Published: 17.04.2018; Views: 1161; Downloads: 315
.pdf Full text (2,44 MB)

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