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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Additive families of Borel sets
 Hronek, Radek ; Zelený, Miroslav (advisor) ; Spurný, Jiří (referee)
This master thesis focuses on the existence of σ-discrete refinement of point countable Borel additive systems in complete metric spaces. In the first three chapters we deal with the lower Borel classes, namely Gδ-additive, Fσ-additive and Fσδ-additive systems. In all cases we show the existence of σ-discrete refi- nement of the systems and even for Gδ-additive systems we don't need point countability. In the fourth chapter we deal with general Borel additive systems, but we place a limiting condition on the weight of space. In the fifth chapter we present an overview of the results that can be obtained by assuming certain additional axioms. 45
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Sigma-ideal of sigma-porous sets
 Hronek, Radek ; Zelený, Miroslav (advisor) ; Holický, Petr (referee)
This bachelor thesis deals with concepts of porous and σ-porous sets, where we prove some basic properties. First, we define terms on the real axis, in other chapters we generalize them into metric spaces. At the end of the thesis there are several interesting examples. In the first chapter we focus on demonstration that σ-porous sets are sets of the first category. The main result of the chapter is that the Lebesgue measure of the σ-porous sets in the space Rn is 0. In the following chapter we deal with the construction of certain sets in the space of continuous functions, in the second case in the space of the nonempty compact sets in Rn . In both cases we show that given sets are σ-porous.
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