Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Genelleştirilmiş Topoloji | MAT 008 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | It is recommended that students to take Topology I and Topology II courses |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | Doktora |
Dersin Türü | Zorunlu |
Dersin Koordinatörü | Prof.Dr. SOLEY ERSOY |
Dersi Verenler | |
Dersin Yardımcıları | |
Dersin Kategorisi | Alanına Uygun Öğretim |
Dersin Amacı | The aim of this course is to generalize some basic concepts of the topological space and to create infrastructure for the studies of doctoral students in the field of topology. |
Dersin İçeriği | Generalized topologies, regular open and regular closed sets, semi-open and semi-closed sets, pre-open and pre-closed sets, b-open and b-closed sets, generalized topologies and generalized neighborhood systems, complete generalized neighborhood systems, generalized continuity, semi-continuous functions, pre-continuous functions, irresolute functions, pre- irresolute functions, generalized open functions, generalized separation axioms, generalized weak separation axioms, generalized compactness, pre-compact, semi-compact, regular compactness, almost compactness, generalized normal spaces, generalized regular spaces, generalized connectedness. |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/she recalls the fundamental concepts of topology. | Lecture, Question-Answer, Drilland Practice, Brain Storming, Problem Solving, | Testing, Homework, |
2 | He/she generalizes the concepts of continuity, connectedness and compactness. | Lecture, Question-Answer, Discussion, Group Study, Brain Storming, Problem Solving, | Testing, Homework, |
3 | He/she analyzes and classifies the special cases of the generalized concepts. | Lecture, Question-Answer, Discussion, Group Study, Brain Storming, Problem Solving, | Testing, Homework, |
4 | He/she gives examples and contra- examples to each special cases | Lecture, Question-Answer, Discussion, Group Study, Brain Storming, Self Study, Problem Solving, | Testing, Homework, |
5 | He/She compares the concepts of each special case with each other. | Lecture, Question-Answer, Discussion, Drilland Practice, Group Study, Brain Storming, Problem Solving, | Testing, Homework, |
6 | He/She represents and proves related theorems. | Lecture, Question-Answer, Discussion, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Generalized Topologies | |
2 | Regular Open And Regular Closed Sets, Semi-Open and Semi-Closed Sets, Pre-Open and Pre-Closed Sets, b-Open and b-Closed Sets | |
3 | Generalized Topologies and Generalized Neighbourhood Systems | |
4 | Complete Generalized Neighborhood Systems | |
5 | Generalized Continuity | |
6 | Semi-Continuous Functions, Pre-Continuous Functions, Irresolute Functions, Pre- Irresolute Functions | |
7 | Generalized Open Functions | |
8 | Generalized Separation Axioms | |
9 | Generalized Weak Separation Axioms | |
10 | Generalized Compactness | |
11 | Pre-Compactness, Semi-Compactness, Regular Compactness | |
12 | Generalized Normal Spaces | |
13 | Generalized Regular Spaces | |
14 | Generalized Connectedness |
Kaynaklar | |
---|---|
Ders Notu | 1. CSASZAR, A., On generalized neighbourhood systems. Acta Math. Hungar. 121 (2008), no. 4, 395400 |
Ders Kaynakları |
Sıra | Program Çıktıları | Katkı Düzeyi | |||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |||
0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | X | |||||
2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | X | |||||
5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | X | |||||
7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | X | |||||
8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | X | |||||
9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
11 | Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. | X |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ödev | 100 |
Toplam | 100 |
1. Yıl İçinin Başarıya | 20 |
1. Final | 80 |
Toplam | 100 |
AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
---|---|---|---|
Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
Mid-terms | 1 | 20 | 20 |
Assignment | 1 | 10 | 10 |
Final examination | 1 | 30 | 30 |
Toplam İş Yükü | 156 | ||
Toplam İş Yükü / 25 (Saat) | 6,24 | ||
Dersin AKTS Kredisi | 6 |