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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Disintegration of category in the sense of the Kuratowski-Ulam theorem
 Rondoš, Jakub ; Spurný, Jiří (advisor) ; Holický, Petr (referee)
The Fubini theorem and the Kuratowski-Ulam theorem show similarities be- tween the concepts meager set in Polish space and set of zero measure in standard Borel space. Those theorems can be generalized. The Fubini theorem is generali- zed by the Measure disintegration theorem and the Kuratowski-Ulam theorem is generalized by the Category disintegration theorem. The claims of disintegration theorems are analogous and show even more the similarities between meager sets and sets of zero measure. The main aim of this thesis is to prove disintegration theorems and show how Fubini and Kuratowski-Ulam theorems follow. 1
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Topologies defined using ideals
 Dvořáková, Karolína ; Kalenda, Ondřej (advisor) ; Murtinová, Eva (referee)
In this thesis we study the topologies formed by a modification of some given topology using ideals - we focus on localizable and strongly localizable ideals. In the first chapter we use a certain set mapping to define ideal topology, then we show its relation to the initial topology. Next we investigate what properties the elements of ideal obtains in the new topology, for example on certain conditions the ideal becomes exactly the set of all nowhere dense sets in the ideal topology. Finally, we show when the new topology is regular and formulate necessary and sufficient conditions for a set with ideal topology to be a Baire space. In the second chapter we apply the results on concrete examples of ideals and topologies defined by them.
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