Syllabus
1.Introduction: various structures the students have already met. Comparison, special features. Combining structures. Relations and relational systems, some general constructions.
3. Partially ordered sets, generalities: posets, monotone maps, suprema and infima, adjunction.
4. Special posets (requiring specific or all suprema resp. infima, lattices and complete lattices. Fixed point theorems, applications. Distributive lattices, Heyting and Boolean algebras.
5. Algebraic operations, algebras, homomorphisms. Some general constructions (remarks on universal algebra). Varieties of algebras.
6. Structure of spaces. Metric spaces, topological spaces.
7. Remarks on some other types of structures.
8. Common features of some constructions: subobjects, quotients, products, sums, equalizers, etc.
Annotation
Structures the students have already met (relations, algebraic structures, continuity structures), more specific facts, comparison. Various constructions (subobjects, equivalences and congruences, products, sums, etc.) in particular cases, and their common features.
Particular attention will be paid to the structure of partial order, both in its general aspects and in the aspects specifically important for computer science.
Some fundamental facts of category theory.