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 |
| Thesis type: | 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 |
| Date of proceeded defence: | 12.09.2019 |
| Opponents: | 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. |