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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Lattice constructions and Priestley duality
 Hartman, Juraj ; Růžička, Pavel (advisor) ; Tůma, Jiří (referee)
In this thesis after recalling some basic definitions and theorems in category theory, lattice theory and topology we first introduce the so called Stone duality of the category of boolean lattices and the category of boolean topological spaces. Then we introduce its generalization, the so called Priestley duality of the category of bounded distributive lattices and the category of total order disconnected topological spaces. Then we introduce the M3[.] lattice construction and prove that for every bounded distributive lattice L there is an isomorphism from the lattice M3[L] to the lattice of all continuous monotone maps from the Priestley space of L to the lattice M3 with discrete topology. Finally we introduce the so called boolean power, which we generalize to the so called priestley power and we prove that for every natural number n ≥ 3 and every bounded distributive lattice L there is an isomorphism from the lattice Mn to the priestley power of the lattice Mn by the lattice L. 1
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Complexity of sets
 Hartman, Juraj ; Zelený, Miroslav (advisor) ; Spurný, Jiří (referee)
In this thesis we first introduce Borel hierarchy of sets in metric spaces and prove some of its properties. Then for special Borel subsets of special metric spaces (Euclidean space of real numbers and the hyperspace of compact subsets of a Polish space with Vietoris topology) we find out where they are in Borel hierarchy, i. e. we find out the class of Borel hierarchy, in which they are, and such that they are in no smaller class with respect to inclusion, which can be understood as an expression of its complexity. Finally we give an example of a coanalytic subset of the hyperspace of compact subsets of a Polish space, which is not Borel, with the proof of its coanalyticity. Powered by TCPDF (www.tcpdf.org)
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See also: similar author names
2 Hartman, J.
2 Hartman, Jakub
6 Hartman, Jan
3 Hartman, Jaroslav
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