| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Lattice Theory II | MAT614 | Elective | Doctorate degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Halis AYGÜN
Associate Prof. Dr. Banu PAZAR VAROL
Learning Outcomes of the Course Unit
1) Gain the ability of making proof by using algebraic structures
2) Identify the topology of continuous lattices by learning continuous and semi-continuous lattices
3) Explain the concepts of Scott topology and Lawson topology
4) State the relations between Sober spaces and general topological spaces by learning the concept of Sober spaces
5) Explain the topological structures of lattices
6) Follow the academical papers related to the lattice theory
7) Apply the different lattice notions to the fuzzy topological structures
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||||
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||
| Learning Outcomes | ||||||||
| 1 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 2 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 3 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 4 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 5 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 6 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
| 7 | No relation | No relation | No relation | No relation | No relation | No relation | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Lattice Theory I
Course Contents
Candidates are provided with in-depth knowledge on continuous and semi-continuous lattices, algebraic lattices, topology of continuous lattices, Scott topology, Scott continuous functions, LAwson topology, spectral theory of continuous lattices, topological induced, weak irreducible and weak prime elements, Sober spaces and total lattices, Heyting algebras, topological semi-lattices, compact topological semi-lattices, metric and topological lattices.
Recommended or Required Reading
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Language of Instruction
Turkish
Work Placement(s)
Not Required