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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ABC 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.

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - He/she recalls the fundamental concepts of topology. 1 - 2 - 4 - 10 - 15 - A - C -
2 - He/she generalizes the concepts of continuity, connectedness and compactness. 1 - 2 - 3 - 8 - 10 - 15 - A - C -
3 - He/she analyzes and classifies the special cases of the generalized concepts. 1 - 2 - 3 - 8 - 10 - 15 - A - C -
4 - He/she gives examples and contra- examples to each special cases 1 - 2 - 3 - 8 - 10 - 14 - 15 - A - C -
5 - He/She compares the concepts of each special case with each other. 1 - 2 - 3 - 4 - 8 - 10 - 15 - A - C -
6 - He/She represents and proves related theorems. 1 - 2 - 3 - 4 - 14 - 15 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 8:Group Study 10:Brain Storming 15:Problem Solving 14:Self Study 4:Drilland Practice
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
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
2. LEVİNE, N., Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.
3. MASHHOUR, A.S., ABD EL-MONSEF, M.E. and EL-DEEP, S.N., On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53.
4. NJASTAD, O., On some classes of nearly open sets, Pacific J. Math, 15 (1965), 961-970.
5. ABD EL-MONSEF, M.E., EL-DEEP, S.N. and MAHMOUD, R.A., open sets and continuous mappings, Bull Fac. Sci. Assiut Univ. A, A12, (1983), no. 1, 77-90.
6. JAMUNARANI, R. and JEYANTHI, P., Regüler sets in generalized topological spaces, Acta Math. Hungar., 135 (4) (2012), 342-349.
7. ANDRİJEVİC, D., On open sets, Mat. Vesnik, 48 (1996), 59-64.
8. CSASZAR, A., Generalized open sets, Acta Math. Hungar., 75 (1997), no. 1-2, 65-87.
9. CSASZAR, A., Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), no. 4, 351-357.
10. CSASZAR, A., Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), 53-66.
11. EKİCİ, E., On weak structures due to Csaszar, Acta Math. Hungar., 134(4) (2012), 565-570.
12. CSASZAR, A., connected sets, Acta Math. Hungar., 101 (2003), 273-279.
13. SHEN R., A note on generalized connectedness, Acta Math. Hungar., 122 (2009), 231-235.
14. WU X. and ZHU P., A note on connectedness, Acta Math. Hungar., 139 (3) (2013), 252-254.
15. CSASZAR, A., Separation axioms for generalized topologies. Acta Math. Hungar. 104 (2004), no. 1-2, 63-69.

Ders Kaynakları

Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
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

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
Odev 1 30
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(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(s) 6.24
Dersin AKTS Kredisi 6.24
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