COURSE UNIT TITLE

: TOPOLOGICAL VECTOR SPACES

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 4058 TOPOLOGICAL VECTOR SPACES ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

Mathematics (Evening)
Mathematics

Course Objective

This course introduces students to the idea of thinking the two concepts topology and vector spaces together.

Learning Outcomes of the Course Unit

1   Will be able to express vector spaces as topological spaces
2   Will be able to know properties of convex sets
3   Will be able to separate convex sets
4   Will be able to know Hahn-Banach theorem and its consequences
5   Will be able to know the L_p-spaces and their properties

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Normed vector spaces, Norm isomorphism, Banach spaces
2 Quotient spaces and topological product, The dual space, Continuous linear mappings
3 The spaces c_0, c and l_1, The spaces l_p
4 The (B)-spaces of holomorphic and continuous functions, The spaces L_p (p>1) .
5 Definitions of topological vector spaces, Completion
6 Quotient spaces and topological products, Finite dimensional topological vector spaces
7 Bounded and compact subsets, locally compact topological spaces
8 Topologically complementary spaces
9 The dual space, hyperplanes, the spaces L_p with 0
10 Metrizable spaces, The Banach-Schauder theorem and the closed graph theorem, Equicontinuous mappings, The theorems of Banach and Banach-Steinhaus, Bilinear mappings
11 The convex and absolutely convex cover of a set, The algebraic boundary of a convex sets, Half spaces
12 Convex bodies and Minkowski functional, Covexcones, Hypercones
13 Seperation theorem, The Hahn-Banach theorem, The analytic proof of Hahn-Banach theorem and its two consequences
14 Supporting hyperplanes, The Hahn-Banch theorem for Normed vector spaces, Adjoint mappings, The dual space of C(I)

Recomended or Required Reading

Textbooks:
1. Köthe, G., Topological Vector Spaces I, Springer, 1969, ISBN 978-0387045092
2. Lawrence, N., Topological Vector Spaces, Springer, 1985, ISBN 0824773152
Materials:
Özçelik, Ahmet Z., Topoloji Ders Notları

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 ASG ASSIGNMENT
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE MTE * 0.40 + ASG * 0.10 + FIN * 0.50
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + ASG * 0.10 + RST * 0.50


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

40% (Midterm examination) +%10(Homework assignment)+50% (Final examination)

Language of Instruction

English

Course Policies and Rules

The student is responsible for attending 70% of the courses throughout the semester. Action will be taken within the framework of the relevant regulations regarding unethical behavior that may occur in classes and exams. You can obtain the DEU Faculty of Science teaching and exam practice principles regulation from http://web.deu.edu.tr/fen.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Phone: +90 232 301 8585
Office: B212 (Mathematics Department)

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 4 56
Preparations before/after weekly lectures 13 3 39
Preparation for midterm exam 1 20 20
Preparation for final exam 1 25 25
Preparing assignments 4 8 32
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 176

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.1443
LO.2443
LO.344433
LO.4433
LO.5443

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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