Thesis (Selection of subject)Thesis (Selection of subject)(version: 290)
Assignment details
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Svazové konstrukce a dualita Priestleyové
Thesis title in Czech: Svazové konstrukce a dualita Priestleyové
Thesis title in English: Lattice constructions and Priestley duality
Key words: kategorie, svaz, topologický prostor
English key words: category, lattice, topological space
Academic year of topic announcement: 2017/2018
Type of assignment: diploma thesis
Thesis language: čeština
Department: Department of Algebra (32-KA)
Supervisor: doc. Mgr. Pavel Růžička, Ph.D.
Author: hidden - assigned and confirmed by the Study Dept.
Date of registration: 23.11.2017
Date of assignment: 19.12.2017
Confirmed by Study dept. on: 03.01.2018
Date and time of defence: 12.09.2019 10:00
Date of electronic submission:19.07.2019
Date of submission of printed version:19.07.2019
Reviewers: doc. RNDr. Jiří Tůma, DrSc.
 
 
 
Guidelines
Cílem práce bude studovat svazové a polosvazové konstrukce odvozené od tensorového součinu polosvazů a popis funktoru odpovídajícího tensorování distributivním svazem pomocí duality mezi kategoriemi distributivních svazů a částečně uspořádaných Stoneových prostorů.
References
Priestley, H. A. (1970). Representation of distributive lattices by means of ordered Stone spaces.Bull. London Math. Soc., (2) 186–190.
Priestley, H. A. (1972). Ordered topological spaces and the representation of distributive lattices. Proc. London Math. Soc., 24(3) 507–530.
Grtzer, G. and Wehrung, F., Proper congruence-preserving extensions of lattices, Acta Math. Hungar. 85 (1999), 175–185.
Grätzer, G. and Wehrung, F., Tensor products of lattices with zero, revisited, J. Pure Appl. Algebra 147 (2000), 273–301.
Grätzer, G. and Wehrung, F., Tensor products and transferability of semilattices, Canad. J. Math. 51 (1999), 792– 815.
Grätzer, G. and Wehrung, F., A new lattice construction: the box product, J. Algebra 221 (1999), 315–344.
Grätzer, G. and Wehrung, F., Flat semilattices, Colloq. Math. 79 (1999), 185–191.
Grätzer, G. and Wehrung, F., The M3[D] construction and n-modularity, Algebra Univers. 41 (1999), 87–114.
Mokriš, S. and Růžička, P., Non-uniqueness of maximal Boolean sublattices in infinite complemented modular lattices. To appear in Algebra Universalis.
Preliminary scope of work
Student si osvojí dvě odlišné oblasti matematiky: teorii svazů a teorii kategorií. V případě úspěšného zvládnutí tématu je šance získat nové publikovatelné výsledky.
Preliminary scope of work in English
Student should learn and apply two distinct subjects: lattice theory and category theory. There is a good chance to obtain new, possibly publishable, results.
 
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