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Lelkova hypotéza
Bartošová, Dana ; Simon, Petr (advisor) ; Balcar, Bohuslav (referee)
Lelek's conjecture which states that metric continua with span zero are chainable has been one of the most widely investigated problems in continuum theory over the past 40 years. We broaden our field of interest to non-metric continua and prove that if there is a non-metric counterexample to Lelek's conjecture we can convert it to a metric one. For a continuum X we take the lattice of all of its closed subsets 2X and consider a countable elementary sublattice L of 2X that we represent by a metric continuum wL via the Wallman representation for distributive lattices. By means of set theory, we obtain an L such that X is not chainable if and only if wL is not chainable and X has span zero if and only if wL has span zero. In the proof of the latter we use Shelah's theorem stating that every two elementarily equivalent models have isomorphic ultrapowers.
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Relative topological properties
Chodounský, David ; Simon, Petr (referee) ; Murtinová, Eva (advisor)
In this thesis we study the concepts of relative topological properties and present some basic facts and relations between them. Our main focus is on various versions of relative normality, relative regularity and relative compactness. We give examples which answer some open questions and contradict some conjectures in the literature. The theory of relative topological properties was introduced by A. V. Arhangel'skii and H. M. M. Genedi in 1989. Our main results are (1) an example which presents a way to modify any Dowker space to get a normal space X such that X × [0, 1] is not -normal (Example 4.2.12). (2) A theorem which implies the existence of a non-Tychonoff space that is internally compact in a larger regular space (Theorem 5.2.8), and (3) a theorem that characterizes couples of closed subsets of the Niemytzki plane which cannot be separated by open sets (Theorem 4.3.4).
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Lebesgue density theorem for Haar measure
Sterzik, Marek ; Zahradník, Miloš (referee) ; Simon, Petr (advisor)
In this work, we study Lebesgue theorem analogy in the space 2k with Haar measure and a related theorem about -k-linkedness of the measure algebra of this space. The whole text is divided in three chapters. In the first chapter we explain some important definitions and basic properties of the measure space. The Lebesgue theorem is studied in the second chapter. After the essential definition of the point of density, the major part of the chapter is dedicated to the proof of the theorem. The theorem states, that the symmetric difference between any measurable set and the set of its points of density has measure zero. In the third chapter we study the -k-linkedness theorem; a theorem which states that the measure algebra of the space 2 is -k-linked, if 2 .
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The business models of IT startups based on sharing economy
Šimon, Petr ; Matuštík, Ondřej (advisor) ; Srpová, Jitka (referee)
The aim of this master thesis is to analyze the present condition of sharing economy and design a critical success factors model on a IT startups which operate as a transportation network companies. The result is finally validated on few representative businesses. The problem is solved by the modified qualitative critical success factors method whose author is John F. Rockart. The gained factors were finally used in the causal model which is based on the principles of system dynamics. The outcomes of this thesis are enabling to understand the relations which are hidden behind success of transportation network companies in the area of sharing economy. The information can be useful not only for startups but also for academic sphere and possible investors.
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ZX Spectrum Small Home Computer Emulator
Šimon, Petr ; Šimek, Václav (referee) ; Růžička, Richard (advisor)
Eight-bit computer ZX Spectrum has been created 30 years ago. It was extremely popular in its time and it has many fans till now, which still developing new application and games. There are also many new hardware extensions like IDE HDD driver, SD/MMC memory driver etc. The aim of this thesis is the design and develop of ZX Spectrum emulator, which will be based on modern PFGA technology and it will use modern periphery like VGA monitor, SD/MMC memory cards etc.
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Simulation of the 8051 Microprocessor Architecture
Šimon, Petr ; Křoustek, Jakub (referee) ; Hruška, Tomáš (advisor)
More than 90% of processors are used in embedded systems today. Processor design for embedded systems is becoming complicated, so it should be automate as much as possible. This bachelor thesis deals with design of the microcontroller 8051. Design is created according to available documentation and ISAC language is used for model description. Results of model simulations are analyzed at the end of this thesis.
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Business plan for a mediating portal
Šimon, Petr ; Bruckner, Tomáš (advisor) ; Chlapek, Dušan (referee)
The aim of this bachelor thesis is to develop a business plan and design a web site that will mediate translations in unconventional way. The resulting document can serve as a template for business plan implementation. First, the thesis provides information on creating a business plan and it also explores the principle of crowdsourcing, which serves as a foundation for the service. The actual business plan is presented as well as the proposal for the web interface, which includes a description of user roles and database structure. The main contribution of this thesis is that it spreads awareness of business models based on crowdsourcing and creates a practical business plan. Readers can then use this business plan as well the provided information base as an inspiration for creating their own.
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