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Two constructions of continua: inverse limits and compactifications
Tina Sovič, 2013, doktorska disertacija

Opis: 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.
Ključne besede: 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
Objavljeno: 25.09.2013; Ogledov: 1305; Prenosov: 82
.pdf Celotno besedilo (861,84 KB)

Suzana Miljević, 2016, diplomsko delo

Opis: Implementation of early foreign language learning in the national curriculum for primary education has been a significant and a popular issue among the language researchers, all the professionals involved in the process of early education and parents. The modern theories and research propose early foreign language learning in primary schools as highly beneficial, crucial and necessary in a sense of spontaneous language acquisition through simple and non-demanding tasks, which are primarily based on auditory perception and physical response as production. In contrast to popular approaches in early foreign language teaching, based on the relation between the tasks’ difficulties and language acquisition, this thesis explores the connection and defines the importance of the attention span in relation to successful language acquisition, in comparison to the importance of the task difficulty. The research was carried out at the Primary School Ljubečna among the second and third grade students, who took part in the listening and reading comprehension examination, which was structured for attention observation and measurement purposes. Each group of the second and the third grade students took a listening and a reading comprehension test. The results and observations of the testing were shown to lead to accurate determinations of the attention influence on early language acquisition. This indicates that there is a possibility that the early reading and writing are not adverse to the process of early foreign language learning and foremost that difficulty of tasks is not in a directly proportional relation to perception and production, namely less demanding tasks are not necessarily completed more successfully than tasks that are more complex.
Ključne besede: KEY WORDS: early learning, early teaching, foreign language, language acquisition, perception, production, attention, attention span, difficulty of tasks, attention observation, attention measurement
Objavljeno: 08.09.2016; Ogledov: 545; Prenosov: 26
.pdf Celotno besedilo (1,92 MB)

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