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  • Course Information
    • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Connected Spaces MAT425 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-Identifies the connected sets and the connected spaces.
    2-Analyzes connectivity on the real line and continuous functions.
    3-Comments the concepts of local and path-connected spaces.
  • ECTS / WORKLOAD
    • ActivityPercentage

    (100)

    		NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14342
    Classroom study (Pre-study, practice)14798
    Assignments0000
    Short-Term Exams (exam + preparation) 10144
    Midterm exams (exam + preparation)30188
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 6011616
    0000
    Total Workload (hours)   168
    Total Workload (hours) / 30 (s)     5,6 ---- (6)
    ECTS Credit   6
  • Course Content
    • Week Topics Study Metarials
    1 Connected sets R2-Section 12
    2 Connected spaces R2-Section 12
    3 Connected space examples R2-Section 12
    4 Connected subspaces R2-Section 12
    5 Connected subsets of real numbers R1-Section 8
    6 Connectivity and continuous functions R1-Section 8
    7 Connectivity of product spaces R2-Section 12
    8 Connected components R1-Section 8
    9 Completely disconnected spaces R2-Section 12
    10 Locally connected space R2-Section 12
    11 Path connected space R2-Section 12
    12 Examples of local and path-connected spaces R1-Section 8
    13 Path connected subset R2-Section 12
    14 Path components R2-Section 12
    Prerequisites -
    Language of Instruction Turkish
    Responsible Assoc. Prof. Dr. Gonca DURMAZ GÜNGÖR
    Instructors -
    Assistants
    Resources R1. Başkan, T., Bizim, O., Cangül İ.N. (2006). Metrik Uzaylar ve Genel Topolojiye Giriş, Nobel Akademik Yayıncılık, Ankara. R2.Koçak, M. (2015) Genel Topolojiye Giriş ve Problem Çözümleri, Nisan Kitapevi, Eskişehir.
    Supplementary Book SR1. Jain, P. K. and Ahmad, K. (2004). Metric spaces. Alpha Science Int`l Ltd. SR2. Kılıç, S. A., Erdem M. (1999). Metrik Uzaylar ve Topoloji, Vipaş Yayınları, İstanbul. SR3. Soykan, Y., (2012). Metrik Uzaylar ve Topolojisi, Nobel Akademik Yayıncılık, Ankara.
    Goals Identifies the concepts of connected set and connected space. Comments the connectivity of real numbers and product spaces. Explains the relationship between local connectivity and path connectivity.
    Content Connected sets, connected spaces, examples of connected spaces, connected subspaces, connected subsets of real numbers, connectivity and continuous functions, connectivity of product spaces, connected components, completely disconnected spaces, locally connected space, path connected space, local and path connected space examples, path-connected subset, path components.
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