Bologna Information System

  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Learning Outcomes
    1-To comprehend the concept of topological space and related basic notions
    2-To comprehend subspace, base and subbase
    3-To expalin the generalizations of basic notions encountered in analysis to an arbitrary topological
    4-To comprehend the notion of continuity and homeomorphism
  • ActivityPercentage


    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)14570
    Short-Term Exams (exam + preparation) 102612
    Midterm exams (exam + preparation)3011414
    Laboratory 0000
    Final exam (exam + preparation) 5011414
    Other 0000
    Total Workload (hours)   178
    Total Workload (hours) / 30 (s)     5,93 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 Basic concepts, sets, functions, relations, countable sets, ordered sets
    2 Topology definition and examples
    3 Subspaces, open and closed sets
    4 Metric topology and examples
    5 ℝ usual space, open and closed sets
    6 Base and subbase for a topology
    7 Neighborhood of a point and local base of a set in topological spaces
    8 Limit point and closure of a set in topological spaces
    9 Interior and isolated point of a set in topological spaces
    10 Dense set and boundary of a set
    11 Continuity in topological spaces
    12 Some real valued functions
    13 Open-closed functions
    14 Homeomorphisms
    Prerequisites --
    Language of Instruction Turkish
    Course Coordinator Assist. Prof. Dr. Gonca DURMAZ
    Instructors -
    Assistants -
    Resources Genel Topolojiye Giriş ve Çözümlü Alıştırmalar (3. Baskı), Mahmut Koçak, 2011.
    Supplementary Book [1] Genel Topoloji (7. Baskı), Şaziye Yüksel, Eğitim Akademi Yayınları, 2011 [2] Topolojik uzaylar, Abdugafur Rahimov, Seçkin Yayınları, 2006. [3] Topology (2nd Edition), James R. Munkres, Prentice Hall, Upper Saddle River, 2000 [4] Basic Topology (Undergraduate Texts in Mathematics), M. A. Armstrong, Springer-Verlag, New York, 2010 [5] Elementary Topology Problem Textbook, O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, American Mathematical Society, 2008. [6] General Topology (Schaums`s Outline Series), Seymour Lipschutz, McGraw-Hill, 2011 A General Topology Workbook, Iain T. Adamson, Birkhauser, Boston, 1996.
    Document Lecture Notes
    Goals Introducing the concept of topological space, demonstrating that real spaces studied in analysis courses are a topological space example and that many basic concepts and properties in these spaces can be generalized to any topological space
    Content -
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 5
    2 To have the ability of abstract thinking 5
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 5
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life 2
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 3
    6 To be able to work compatibly and effectively in national and international groups and take responsibility -
    7 To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge 4
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 4
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time 2
    10 To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally 4
    11 To be able to produce projects and arrange activities with awareness of social responsibility -
    12 To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level -
    13 To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results -
    14 To have the awareness of acting compatible with social, scientific, cultural and ethical values -
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