Soft Topological Spaces
Mathematics
Institute of Natural and Applied Sciences
Third Cycle (Doctorate Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Soft Topological Spaces | MAT625 | Elective | Doctorate degree | 1 | Spring | 8 |
Name of Lecturer(s)
Prof. Dr. Halis AYGÜN
Associate Prof. Dr. Vildan ÇETKİN
Associate Prof. Dr. Banu PAZAR VAROL
Learning Outcomes of the Course Unit
1) State the soft topology.
2) Explain the soft topological structures
3) State the fuzzy soft topology.
4) Explain the fuzzy soft topological structures.
5) State the fuzzifying soft topological space.
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 | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Topology 1, Topology 2
Course Contents
Soft topological spaces, fuzzy soft topological spaces, fuzzifying soft topological spaces with the notions of base, subbase and the topological structures such as neighborhood systemsi interior and closure operators, compactness and separation axioms.
Weekly Schedule
1) Soft topological space, subbase, base2) Neighborhood system of soft topological spaces, soft interior and closure operators
3) Continuity and compactness in soft topological spaces
4) Separation axioms of soft topological spaces
5) Topology of fuzzy soft sets, subbase, base and continuity
6) Neighborhood system in the topology of fuzzy soft sets, interior and closure operators
7) Separation axioms of the topology of fuzzy soft sets
8) Midterm/Assesment
9) Fuzzy soft topology, subbase, base
10) Continuity in the fuzzy soft topological spaces and neighborhood systems
11) Fuzzy soft interior and closure operators
12) Separation axioms in fuzzy soft topological spaces
13) Compactness in fuzzy soft topological spaces
14) Fuzzfying soft topological spcaes
15) Categorical relations among soft topological spaces
16) Final examination
Recommended or Required Reading
1- Esnek Topolojik Uzaylar, Abdülkadir Aygünoğlu, Doktora Tez, KOÜ Fen Bilimleri Enstitüsü
2- Some Notes on Soft Topological Spaces, Neural Comput.& Applic., 2012
3- Fuzzy Soft Topology, Hacettepe Journal of Mathematics and Statistics, 2012
Planned Learning Activities and Teaching Methods
1) Lecture
2) Question-Answer
3) Discussion
4) Group Study
5) Self Study
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
40% |
|---|---|
Contribution of Final Examination to Course Grade |
60% |
Total |
100% |
Language of Instruction
Turkish
Work Placement(s)
Not Required