Neste trabalho, veremos que a noção de número de Nielsen pode ser estendida para aplicações entre variedades topológicas não necessariamente orientáveis ou compactas, com ou sem fronteira. / In this work, we are going to see that the concept of Nilsen Root Number can be extended to maps between not necessarily orientable nor compact manifolds, with or without boundary.

This diploma thesis entitled "The history of guild crafts in a town Krupka" aims to bring the origin, development and functioning of craft guilds which operated in the town Krupka. The main aim of this diploma thesis is to analyze the content of guild orders, guild books and file material from different perspectives, which are described in detail in the chapters, in which the work is divided. The chapter sources and literature reflects the important archival sources related to guilds in a general scale for the territory of Krupka and the chapter also informs about the basic issued publications, that are thematically bind to the guild organizations, their development and functioning. The following section outlines the administrative development in the town Krupka. At the core is the chapter dealing with the guild craft in Krupka from different angles and perspectives. The annexes attached to this thesis is complemented with information referred to in the text of the work, and are composed mainly of namespaces of craftsmen.

Στα δύο πρώτα κεφάλαια γίνεται μια ιστορική αναδρομή και αναφέρονται όλες οι απαραίτητες εισαγωγικές έννοιες που χρειάζονται έτσι, ώστε να γίνει απρόσκοπτα και χωρίς ασάφειες το κυρίως μέρος της εργασίας. Στο κεφάλαιο τρία περιγράφονται και αναλύονται οι συμπαγείς τοπολογικοί χώροι. Κατά σειρά εξετάζονται οι συμπαγείς χώροι, οι συνεχείς απεικονίσεις πάνω σε συμπαγείς χώρους και τέλος οι τοπικά συμπαγείς χώροι. Επίσης περιγράφονται έννοιες συναφείς με τη συμπάγεια. Στο τέταρτο και τελευταίο κεφάλαιο ορίζεται η έννοια της συμπαγοποίησης ενός τοπολογικού χώρου και μελετώνται κατά σειρά η συμπαγοποίηση ενός σημείου, η συμπαγοποίηση Stone – Čech και η Wallman-type συμπαγοποίηση. / We study compact topological spaces. We also describe the compactification of a topological space. Especially we describe the Alexandroff, Stone-Cech and Wallman type compactifications.

The main task of this thesis is to summarize the diplomatics material of guild corporations at Havlíčkův Brod area into integrated form. Bacause of broad topic, the selection was only focused on the textile craft occurring in this region and especially in deeds. In the introducion the work presents history of the guilds from their beginning to the final downfall - focusing on textile production. It summarizes the genaral situation of the surviving monuments. The edition which is created from deeds issued by these corporations and also by publishers for mentioned guilds - this is the main core of the thesis. The deeds are arranged chronologically according particular guilds and towns. They are completed by diplomatic analysis of internal and external signs and by the final study, which summarizes all the research.

(in English): This master thesis follows the history of Prague guilds from the very beginning of their system to the end in 1860. Research was focused on cities which created former Prague - Old Town, New Town, Lesser Town and Hradčany. At first, used sources and their evaluation for the above mentioned research are described. There are reflections of the most important moments in the history of guilds in the Czech Lands, especially in Prague towns at that time, in the next chapters. Main goal of this thesis is to reconstruct a picture of all historical guilds and brotherhoods in the cities of Prague. My own research reflects knowledge of previous researchers. These were thereafter compared to some new sources and revised. Unknown parts of the history of Prague guilds were elaborated, such as history of this system in modern period. Based on some particular knowledge of history of singular guilds new hypotheses of general evolution of guilds in Prague were formed. Attached are glossaries of names of professions (Latin, German and Old Czech), that were in Prague towns in the past.

The Abstract The present work deals with the guilds, which operate on the territory of Uherský Brod from its inception to the year 1859, when the guilds were replaced by trade licensing crafts. The introductory part brings the history of the city itself and guild system. An important milestone in the life of the guilds became the release of the general guild patent and articles. Said instruments are described in separate chapters. The main part is divided into five groups according to the orientation of individual trades, which is an attempt to answer questions about the formation of the guild and its development from archival sources. Emphasis was placed on the analysis guild articles. The work is accompanied by a picture attachment with preserved guild objects. Powered by TCPDF (www.tcpdf.org)

This diploma thesis deals with brewing and malting as a way of livelihood of ecclesiastical and secular goods in the territory of the Czech kingdom. This work is also aimed at showing our traditional and national beverage as an important part of our culture and tradition. It wants to introduce beer not only as an alcoholic beverage, but mainly as a business article. Its production and trading with it has been a source of high income not only in the treasuries of cities and nobility, but also in the treasuries of the church. As an example of the Church Brewery, the Conventional Brewery was chosen in Vyšší Brod. The first chapter of the work attempts to show the history of beer brewing closer. The thesis does not aim to describe the history of beer production, but to focus on the first references to it and the production methods used from the oldest cultures, such as Mesopotamian, Babylonian or Egyptian, to our closest Slavonic culture. Another chapter tries to map the production of beer and the struggle for it on the territory of the Czech Crown in the period of its rise, prosperity and mild decline in the middle of the seventeenth century. The last chapter is focused on the Conventional Brewery in Vyšší Brod, which was chosen as a characteristic example for the selected theme and above all as a monument...

This thesis is divided into two parts: Ordered spaces of Continuous Functions and the algebras associated with the topology of pointwise convergence of the associated construct, and Strictly completely regular bitopological spaces. The Motivation for part of the first part (Chapters 2, 3 and 4) comes from the recent study of function spaces for bitopological spaces in [44] and [45]. In these papers we see a clear generalisation of classical results in function spaces ( [14] and [55]) to bi-topological spaces. The well known definitions of the pointwise topology and the compact open topology in function spaces are generalized to bitopological spaces, and then familiar results such as Arens' theorem are generalised. We will use the same approach in chapters 2, 3 and 4 to formulate analogous definitions in the setting of ordered spaces. Well known results, including Arens' theorem, are also generalised to ordered spaces. In these chapters we will also compare function spaces in the category of topological spaces and continuous functions, the category of bi topological spaces and bicontinuous functions, and the category of ordered topological spaces and continuous order-preserving functions. This work has resulted in the publication of [30] and [31]. Continuing our study of Function Spaces, we oonsider in Chapters 5 and 6 some Categorical aspects of the construction, motivated by a series of papers which includes [39], [40], [41] and [50]. In these papers the Eilenberg-Moore Category of algebras of the monad induced by the Hom-functor on the categories of sets and categories of topological spaces are classified. Instead of looking at the whole product topology we will restrict ourselves to the pointwise topology and give examples of the EilenbergMoore Algebras arising from this restriction. We first start by way of motivation, with the discussion of the monad when the range space is the real line with the usual topology. We then restrict our range space to the two point Sierpinski space, with the aim of discovering a topological analogue of the well known characterization of Frames as the Eilenberg-Moore Category of algebras associated with the Hom-F\mctor of maps into the Sierpinski space [11]. In this case the order structure features prominently, resulting in the category Frames with a special property called "balanced" and Frame homomorphisms as the Eilenberg-Moore category of M-algebras. This has resulted in [34]. The Motivation for the second part comes from [20] and [15]. In [20], J. D. Lawson introduced the notion of strict complete regularity in ordered spaces. A detailed study of this notion was done by H-P. A. Kiinzi in [15]. We shall introduce an analogous notion for bitopological spaces, and then shall also compare the two notions in the categories of bi topological spaces and bicontinuous functions, and of ordered topological spaces and continuous order-preserving functions via the natural functors considered in the previous chapters. We further study the Stone-Cech bicompactification and Stone-Cech ordered compactification in the two categories. This has resulted in [32] and [33] / Mathematical Sciences / D. Phil. (Mathematics)

<p>This dissertation establishes a variety of limit theorems pertaining to rare events in stochastic topology, exploiting probabilistic methods to study simplicial complex models. We focus on the filtration of \vc ech complexes and examine the asymptotic behavior of two topological functionals: the Betti numbers and critical faces. The filtration involves a parameter rn>0 that determines the growth rate of underlying Cech complexes. If rn depends also on the time parameter t, the obtained limit theorems will be established in a functional sense.</p> <p>The first part of this dissertation is devoted to investigating the layered structure of topological complexity in the tail of a probability distribution. We establish the functional strong law of large numbers for Betti numbers, a basic quantifier of algebraic topology, of a geometric complex outside an open ball of radius Rn, such that Rn to infinity as the sample size n increases. The nature of the obtained law of large numbers is determined by the decay rate of a probability density. It especially depends on whether the tail of a density decays at a regularly varying rate or an exponentially decaying rate. The nature of the limit theorem depends also on how rapidly Rn diverges. In particular, if Rn diverges sufficiently slowly, the limiting function in the law of large numbers is crucially affected by the emergence of arbitrarily large connected components supporting topological cycles in the limit.</p> <p>The second part of this dissertation investigates convergence of point processes associated with critical faces for a Cech filtration built over a homogeneous Poisson point process in the d-dimensional flat torus. The convergence of our point process is established in terms of the  Mo-topology, when the connecting radius of a Cech complex decays to 0, so slowly that critical faces are even less likely to occur than those in the regime of threshold for homological connectivity. We also obtain a series of limit theorems for positive and negative critical faces, all of which are considerably analogous to those for critical faces.</p>

Cette thèse d'algèbre commutative porte principalement sur la théorie de la profondeur. Nous nous efforçons d'en fournir une approche épurée d'hypothèse noethérienne dans l'espoir d'échapper aux idéaux premiers et ceci afin de manier des objets élémentaires et explicites. Parmi ces objets, figurent les complexes algébriques de Koszul et de Cech dont nous étudions les propriétés cohomologiques grâce à des résultats simples portant sur la cohomologie du totalisé d'un bicomplexe. Dans le cadre de la cohomologie de Cech, nous avons établi la longue suite exacte de Mayer-Vietoris avec un traitement reposant uniquement sur le maniement des éléments. Une autre notion importante est celle de dimension de Krull. Sa caractérisation en termes de monoïdes bords permet de montrer de manière expéditive le théorème d'annulation de Grothendieck en cohomologie de Cech. Nous fournissons également un algorithme permettant de compléter un polynôme homogène en un h.s.o.p.. La profondeur est intimement liée à la théorie des résolutions libres/projectives finies, en témoigne le théorème de Ferrand-Vasconcelos dont nous rapportons une généralisation due à Jouanolou. Par ailleurs, nous revenons sur des résultats faisant intervenir la profondeur des idéaux caractéristiques d'une résolution libre finie. Nous revisitons, dans un cas particulier, une construction due à Tate permettant d'expliciter une résolution projective totalement effective de l'idéal d'un point lisse d'une hypersurface. Enfin, nous abordons la théorie de la régularité en dimension 1 via l'étude des idéaux inversibles et fournissons un algorithme implémenté en Magma calculant l'anneau des entiers d'un corps de nombres. / This Commutative Algebra thesis focuses mainly on the depth theory. We try to provide an approach without noetherian hypothesis in order to escape prime ideals and to handle only basic and explicit concepts. We study the algebraic complexes of Koszul and Cech and their cohomological properties by using simple results on the cohomology of the totalization of a bicomplex. In the Cech cohomology context we established the long exact sequence of Mayer-Vietoris only with a treatment based on the elements. Another important concept is that of Krull dimension. Its characterization in terms of monoids allows us to show expeditiously the vanishing Grothendieck theorem in Cech cohomology.We also provide an algorithm to complete a omogeneous polynomial in a h.s.o.p.. The depth is closely related to the theory of finite free/projective resolutions. We report a generalization of the Ferrand-Vasconcelos theorem due to Jouanolou. In addition, we review some results involving the depth of the ideals of expected ranks in a finite free resolution.We revisit, in a particular case, a construction due to Tate. This allows us to give an effective projective resolution of the ideal of a point of a smooth hypersurface. Finally, we discuss the regularity theory in dimension 1 by studying invertible ideals and provide an algorithm implemented in Magma computing the ring of integers of a number field.