Course Name Code Semester T+U Hours Credit ECTS
Topological Vector Spaces I MAT 507 0 3 + 0 3 6
Precondition Courses <p>Topology I-II</p>
Recommended Optional Courses
Course Language Turkish
Course Level yuksek_lisans
Course Type Optional
Course Coordinator Doç.Dr. MAHPEYKER ÖZTÜRK
Course Lecturers Prof.Dr. SOLEY ERSOY,
Course Assistants
Course Category Available Basic Education in the Field
Course Objective

To apprehend the properties of the topological vector spaces,to learn the local convex topological vector spaces,Convex sets and semi-norms, normed spaces and normable spaces,Hahn-Banach theorem,local convex spaces,projective topologies,reductive topologies,Barrelled spaces,Bornological spaces,Compact Convex sets.

Course Content

Topological vector spaces(TOPOLOGY OF VECTOR SPACES,product spaces,subspace,direct sum,quotient space,topological vector spaces with finite dimension,Linear manifolds and hyperplanes,bounded sets,metrizable,complexification),Local convex topological vector spaces(convex sets and semi norms, normed and normable spaces Hahn-Banach theorem,local convex spaces,projective topologies,reductive topologies,Barrelled spaces,Bornological spaces,Compact Convex sets.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/ she recognizes the Topological vector spaces Lecture, Question-Answer, Discussion, Self Study, Testing, Homework,
2 He/ she explains the local convex topological vector spaces Lecture, Question-Answer, Discussion, Self Study, Testing, Homework,
3 He/ she interprets the convex sets and semi-norms, normed and normable spaces. Lecture, Question-Answer, Discussion, Self Study, Testing, Homework,
4 He/ she recognizes the Local convex spaces, ,Barrelled spaces,Bornological spaces Lecture, Question-Answer, Discussion, Self Study, Testing, Homework,
5 He/ she defines projective topologies and reductive topologies. Lecture, Question-Answer, Discussion, Self Study, Testing, Homework,
6 He/she recognizes the compacy convex sets. Lecture, Question-Answer, Discussion, Self Study, Testing, Homework,
Week Course Topics Preliminary Preparation
1 Topological vector spaces
2 TOPOLOGY OF VECTOR SPACES
3 product spaces,subspace
4 direct sum,quotient space,
5 topological vector spaces with finite dimension
6 Linear manifolds and hyperplanes
7 bounded sets,metrizable,complexification,
8 Local convex topological vector spaces
9 ıntermediate examination
10 convex sets and semi norms
11 normed and normable spaces Hahn-Banach theorem,
12 local convex spaces,projective topologies,reductive topologies
13 Barrelled spaces,Bornological spaces
14 Compact Convex sets.
Resources
Course Notes <p>[1][1] H.&nbsp;H.&nbsp;Schaefer, M.&nbsp;P.&nbsp;Wolff,&nbsp;Topological Vector Spaces,&nbsp;Springer, New York, NY, 1999</p> <p>&nbsp;</p>
Course Resources

[2] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul

[3] Maddox,I.J.; Elements of Functional Analysis, Cambridge Un.Press,1970,London.
[4] Şuhubi, Erdoğan; Fonksiyonel Analiz, İTÜ Vakfı, 2001, İstanbul
[5] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982.

Order Program Outcomes Level of Contribution
1 2 3 4 5
2 Student follows the current journals in his/her field and puts forward problems. X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level.
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 80
1. Ödev 10
2. Ödev 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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 2 10 20
Final examination 1 25 25
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6