|
Week
|
Topics
|
Study Metarials
|
|
1
|
Homeomorphisms, T0 and T1 spaces
|
K1) Chapter 5
|
|
2
|
T2 and T3 spaces
|
K1) Chapter 5
|
|
3
|
T3/2 and T4 spaces
|
K1) Chapter 5
|
|
4
|
First and second countable spaces
|
K2) Lecture Notes Section 1
|
|
5
|
Separable and Lindelöf spaces
|
K2) Lecture Notes Section 2
|
|
6
|
Continuity in topological spaces
|
K2) Lecture Notes Section 3
|
|
7
|
Product spaces
|
K1) Chapter 2
|
|
8
|
Quotient spaces
|
K2) Lecture Notes Section 4
|
|
9
|
Networks
|
K2) Lecture Notes Section 5
|
|
10
|
Compact Spaces
|
K2) Lecture Notes Section 6
|
|
11
|
Countably and sequentially compact spaces
|
K2) Lecture Notes Section 7
|
|
12
|
Compactness in metric spaces
|
K2) Lecture Notes Section 8
|
|
13
|
Connected spaces
|
K2) Lecture Notes Section 9
|
|
14
|
Connectedness and continuous functions
|
K2) Lecture Notes Section 10
|
|
Prerequisites
|
-
|
|
Language of Instruction
|
English
|
|
Responsible
|
Assoc. Prof. Dr. Mustafa ASLANTAŞ
|
|
Instructors
|
-
|
|
Assistants
|
-
|
|
Resources
|
K1) General Topology, Stephen Willard, Addison-Wesley,1970.
K2) Lecture Notes
|
|
Supplementary Book
|
YK1) General Topology, Seymour Lipschutz, Shaum`s outline, 1965.
YK2) General Topology, Ryszard Engelking, Helderman Verlag Berlin, 1989.
|
|
Goals
|
To introduce topological concepts, to give property of topological spaces
|
|
Content
|
Separation axioms, countabile spaces, separable spaces,Convergence in topological spaces, networks, Product spaces, partition spaces, Compact spaces, compactness of subspaces,Closed set and Compact subsets of R-standard space, Compactness and continuous function.
|
|
Program Learning Outcomes |
Level of Contribution |
|
1
|
Having advanced theoretical and applied knowledge in the basic areas of mathematics
|
-
|
|
2
|
Ability of abstract thinking
|
3
|
|
3
|
To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
|
3
|
|
4
|
Associating mathematical achievements with different disciplines and applying them in real life
|
-
|
|
5
|
Ability to work independently in a problem or project that requires knowledge of mathematics
|
-
|
|
6
|
Ability to work harmoniously and effectively in national or international teams and take responsibility
|
-
|
|
7
|
Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
|
-
|
|
8
|
To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
|
3
|
|
9
|
To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
|
-
|
|
10
|
Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
|
-
|
|
11
|
Being able to produce projects and organize events with social responsibility awareness
|
-
|
|
12
|
Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
|
-
|
|
13
|
Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
|
-
|
|
14
|
Being conscious of acting in accordance with social, scientific, cultural and ethical values
|
-
|