National Repository of Grey Literature 32 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
Homogeneity of topological structures
Vejnar, Benjamin ; Hušek, Miroslav (advisor) ; Pyrih, Pavel (referee)
In the present work we study those compacti cations such that every autohomeomorphism of the base space can be continuously extended over the compacti cation. These are called H-compacti cations. We characterize them by several equivalent conditions and we prove that H-compacti cations of a given space form a complete upper semilattice which is a complete lattice when the given space is supposed to be locally compact. Next, we describe all H-compacti cations of discrete spaces as well as of countable locally compact spaces. It is shown that the only H-compacti cations of Euclidean spaces of dimension at least two are one-point compacti cation and the Cech-Stone compacti cation. Further we get that there are exactly 11 H-compacti cations of a countable sum of Euclidean spaces of dimension at least two and that there are exactly 26 H-compacti cations of a countable sum of real lines. These are all described and a Hasse diagram of a lattice they form is given.
Aplikace Baireovy věty
Peprníková, Ľubica ; Simon, Petr (advisor) ; Pyrih, Pavel (referee)
The aim of this work is to show, having three di®erent spaces and a set of elements with some common property in each one of them that the given set is the set of typical elements in that space. First we will show that a typical continuous function deffined on the interval [0; 1] is a nowhere differentiable one. Then we will show that a typical compact set in R2 is a discontinuum. And lastly, we will show that a typical planar continuum is an indecomposable one. A valuable tool will be the Baire theorem, the use of which will ensure, besides the density, also the fact that the given set is a countable intersection of open sets.
Homeomorphisms in topological structures
Vejnar, Benjamin ; Pyrih, Pavel (advisor) ; Charatonik, Włodzimierz (referee) ; Illanes, Alejandro (referee)
In this thesis, we present solutions to several problems concerning one-dimensi- onal continua. We give an inductive description of graphs with a given disconnec- tion number, this answers a question of S. B. Nadler. Further, we state a topo- logical characterization of the Sierpi'nski triangle. In the study of shore sets in dendroids and λ-dendroids we obtain several positive results and we also provide some counterexamples. By doing this, we continue in the recent work of several authors. We are also dealing with the notion of 1 2 -homogeneity and we prove that up to homeomorphism there are only two 1 2 -homogeneous chainable continua with just two end points. We present also a new elegant proof of a classical theorem of Waraszkiewicz. 1
Monotonicity of functions which can be expressed using elementary functions
Peltan, Libor ; Bárta, Tomáš (advisor) ; Pyrih, Pavel (referee)
For certain types of functions expressible with formula (equivalently: functions from classes closed to arithmetic operations) under stated assumptions, we prove monotonicity at some neighbourhood of +∞. They are: formulas containing exp, log, sin, arctan, etc. with constrainted domain of these functions; power series with cofinite many coefficients positive; various classes of functions expressible with formulas with the requirement of preserving monotony in summation, or multiplication, or the monotony resulting from having a finite number of zero points; and finally formulas with square root. 1
Extension of mappings into Banach spaces
Novotný, Vojtěch ; Hušek, Miroslav (advisor) ; Pyrih, Pavel (referee)
This diploma thesis deals with extending continuous and uniformly continuous mappings. It studies Lebesgue's and Tietze's work in metric spaces through Urysohn's theorem in normal topological spaces, Kat etovs' papers about uniformly continuous functions up to Dugundji's theorem and relationship between continuous extending of pseudometrics and mappings. It connects the articles of nineteen mathematicians of the twentieth century, presents plenty of theorems in more general form and shows that they could be formulated earlier or proved in another way.
Open problems in Continuum thory
Seifrt, Jan ; Pyrih, Pavel (advisor) ; Spurný, Jiří (referee)
ISYixev prace: Otevfene problemy teorie konlinm Autor: Jan Seifrt Katcdra (ustav): Katedra matematicke analyzy Vedouci ba.kaliirske prace: Doc. RNDr. Pavel Pyrih, CSc. e-mail vedouciho: poliodai6.gniail.com Anstrakt: PiYdlo/ena pracc sc /a))yva v/tahrin iiia^iicli('l\ycb a koiH-rnr pn- riodickych bodu v jislycli koiiipaktiiu-li .souvislych mno/iuach. Teziste prace s])ociva v in)di-()l)in''in ro/boru dvou ])ul)liku\>uiycli vyslcdkii (motor a null- comb). Fungovam Irclito ])fikladu JL- /achycono na fade pomocnydi obraxkii. Pia(.:c obsabnjc polrubnc definicr a /aktadni 1 vr/cm' Inv, dukaxu. V praci JHOU dale doka'/ana i dalsi tvr/oni / dam'1 problcmatiky. vii shiva: dcndril., ill]I' vla.st.imsr, ina^iiutickr body a mill-comb Tillc: Open problems in Continuum thmry Author: Jan Scifrt Department.; Department of Matheinal ical Analysis Supervisor: Doc. HNDr. Pavel Pyrili, CSc. Supervisor's e-mail address: Abstract: In t lit1 present work \ve study the relation between non-wandering ami eventually-periodic- points in certain compact conned ed sets. The goal of the work consists of detailed study of two published results (engine and null-comb). How these examples work is demonstrated by a. sequence of fi- gures. The work contain all needed definitions a.nd lacts wit.lumt proofs. In the work are proved some other...
Fundaments of IT thinking
Jelínek, Jakub ; Pyrih, Pavel (advisor) ; Obdržálek, David (referee)
In the propounded work author presents results of his looking for important informatics thinking features, its fundaments. He divides these fundaments into two categories - static and dynamic. Static fundaments represent basic building material that the informatics world is built from. As static fundaments are considered information, time, room and money. Dynamic fundaments express basic "active factors" which are using static fundaments and are transforming them, creating so more complicated elements of informatics. As dynamic fundaments are considered abstraction, iteration and recursion, metasyntactic variables, universality, simplicity and inspiration.
Hausdirff metric and its application in fractals
Roháľ, Branislav Ján ; Hušek, Miroslav (advisor) ; Pyrih, Pavel (referee)
Title: Hausdorff metric and its application in fractals Author: Branislav Ján Roháľ Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Miroslav Hušek, DrSc., Department of Mathematical Analysis Abstract: In this thesis we focus on the themes naturally connected with the con- cept of a fractal. In the first part of the thesis we pay attention to Banach fixed point theorem and to the Hausdorff metric which are later used when studying self-similar sets. There are included parts on the Hausdorff, similarity, and box- counting dimension, too. In the second part of the thesis the new approaches to fractal dimension and some their properties are refered. We introduce generaliza- tion of this concept for any space admitting a fractal structure and for a distance space where also the "size" of sets on each level of fractal structure is considered. In the last chapter the contribution of new approache is demonstrated, - this enables defining the notion needed and counting fractal dimension where it was not possible under the classical approaches, too. Application to the domain of words and counting of dimensions of a language generated by a regular expresion are presented. Keywords: Hausdorff metric, Banach fixed point theorem, self-similar set, Hausdorff dimension, fractal dimension
Future predicting and the axiom of choice
Jarosil, Lukáš ; Pyrih, Pavel (advisor) ; Kalenda, Ondřej (referee)
Given arbitrary function f : R → R it seems practically impossible to predict its future values based on our knowledge of its previous values. Nevertheless, axiom of choice surprisingly implies the existence of strategy that from values of the function f on some interval (s, t) correctly predicts its values on interval [t, t+ ) for every t of real line except for countable set. This result of Christopher Hardin and Alan Taylor is presented along with its generalization to mappings from topological space in the context of hat guessing games, mathematical games in which the players are supposed to guess color of their own hat while knowing only colors of other's hats. 1

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