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Products of Fréchet spaces
Olšák, Miroslav ; Simon, Petr (advisor) ; Chodounský, David (referee)
The article gives a constructions of k-tuples of topological spaces such that the product of the k-tuple is not Frchet-Urysohn but all smaller subproducts are. The construction uses almost disjoint systems. The article repeats the construction by Petr Simon of two such compact spaces. To achieve more dimensional example there are generalized terms of AD systems. The example is constructed under the assumption of existence of a strong completely separable MAD system. It is then constructed under the assumption s ≤ b where s is the splitting number and b is the bounding number.
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Generalizing CSP-related results to infinite algebras
Olšák, Miroslav ; Barto, Libor (advisor) ; Zhuk, Dmitrii (referee) ; Pinsker, Michael (referee)
The recent research on constraint satisfaction problems (CSPs) on fixed finite templates provided useful tools for computational complexity and universal algebra. However, the research mainly focused on finite relational structures, and consequently, finite algebras. We pursue a generalization of these tools and results into the domain of infinite algebras. In particular, we show that despite the fact that the Maltsev condition s(r, a, r, e) = s(a, r, e, a) does not characterize Taylor algebras (i.e., algebras that satisfy a nontrivial idem- potent Maltsev condition) in general, as it does in the finite case, there is another strong Maltsev condition characterizing Taylor algebras, and s(r, a, r, e) = s(a, r, e, a) characterizes another interesting broad class of algebras. We also provide a (weak) Maltsev condition for SD(∧) algebras (i.e., algebras that satisfy an idem- potent Maltsev condition not satisfiable in a module). Beyond Maltsev conditions, we study loop lemmata and, in particular, reprove a well known finite loop lemma by two different general (infinite) approaches.
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Products of Fréchet spaces
Olšák, Miroslav ; Simon, Petr (advisor) ; Chodounský, David (referee)
The article gives a constructions of k-tuples of topological spaces such that the product of the k-tuple is not Frchet-Urysohn but all smaller subproducts are. The construction uses almost disjoint systems. The article repeats the construction by Petr Simon of two such compact spaces. To achieve more dimensional example there are generalized terms of AD systems. The example is constructed under the assumption of existence of a strong completely separable MAD system. It is then constructed under the assumption s ≤ b where s is the splitting number and b is the bounding number.
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Children of 50th years. Family Memory in Families of Political Prisoners
Olšák, Miroslav ; Houda, Přemysl (advisor) ; Doskočil, Zdeněk (referee)
This diploma thesis deals with family memory of 1950s Czechoslovak political prisoners. Its two major questions are: Is there a well preserved story in an actual family memory of a family ancestor who was politically persecuted and imprisoned in the period after 1948 and is his story preserved without significant shifts from reality? Given topic is being analyzed throughout a story of three particular families - those of Bedřich Fučík, Ladislav Jehlička and Karel Procházka. These three political prisoners died already, therefore were the subject of examination records of three generations of their descendents. Primary sources for this thesis are thus personal interviews with these family members. Both archive sources and original texts written byl Bedřich Fučík and Ladislav Jehlička were also used. Individual interviews have shown that a story of their ancestor is well perserved in family memory, but every particular family or narrator have their own specificities. Some narrators have shown major shifts from reality, whereas others have not. Key words political prisoners, 1950s, family memory, communist regime, oral history
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Quadratic word equations
Olšák, Miroslav ; Holub, Štěpán (advisor) ; Stanovský, David (referee)
The article discuses satisfiability of quadratic word equations. It reproduces results of Robson and Diekert and explores the question about simple exponential bound of the shortest solution of quadratic word equations. The positive answer to this question would mean NP completeness of satisfiability of quadratic word equations. The simple exponential bound hypothesis was not solved but some results were given: for example a smaller class of equations which needs to be investigated or a proposition saying that it is sufficient to prove a bound of the smallest variable. At the end of this work the behavior of a particular equations is shown and afterwards the duality of two concepts of quadratic word equations handling is explained. Powered by TCPDF (www.tcpdf.org)
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