Course detail
Ordered Sets and Lattices
FSI-9UMSAcad. year: 2020/2021
Students will get acquainted with basic concepts and results of the theory of ordered sets and lattices used in many branches of mathematics and in other disciplines, e.g., in informatics.
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Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
Steve Roman, Lattices and ordered sets, Springer, New York 2008. (EN)
T.S. Blyth, Lattices and Ordered Algebraic Structures, Springer, 2005 (EN)
Recommended reading
George Grätzer: Lattice Theory: Foundation, Birkhäuser, Basel, 2011 (EN)
L. Beran, Uspořádané množiny, Mladá fronta, Praha,1978 (CS)
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Syllabus
2. Axiom of Choice and equivalent theorems
3. Duality and monotonne maps
4. Down-sets and up-sets, ascending and descending chain conditions
5. Well ordered sets and ordinal numbers
6. Cardinal numbers, cardinal and ordinal arithmetic
7. Closure operators on ordered sets
8. Ideals and filters
9. Modular and distributive lattices
10. Boolean lattices