CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

METRIC SPACES | MAT306 | SPRING | 4+0 | Fac./ Uni. | C | 8 |

Learning Outcomes | 1-To be able explain the concept of topological space and related basic notions 2-To be able to do the generalizations of basic notions encountered in analysis to an arbitrary topological space 3-To be able to explain the notion of continuity 4-To be able to explain the notions of compactness and connectedness |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 8 | 112 | |

Assignments | 10 | 2 | 8 | 16 |

Short-Term Exams (exam + preparation) | 10 | 2 | 8 | 16 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 228 | |||

Total Workload (hours) / 30 (s) | 7,6 ---- (8) | |||

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | The notions of topology and open set, examples of topological spaces; comparison of topologies | |

2 | The usual toplogy of reel numbers; the notion of neighborhood and the family of neighborhoods | |

3 | The position of a point to a set; the definitions and examples of interior, exterior, boundary, accumulation and isolated points | |

4 | The interior, exterior, boundary, isolated points and the closure of a set, and the relations between these notions | |

5 | The basis and subbasis of a topology | |

6 | The notion of continuity, continuity at a point and continuity on a space, the characteristics theorems of a continuity | |

7 | Open and closed functions, homeomorphisms | |

8 | The initial topology and product spaces | |

9 | The final topology and quotient spaces | |

10 | The subspaces, the inherited and topological properties | |

11 | Compactness and compact spaces; compactness of the subspaces; the compact subsets with respect to usual topology of reel numbers | |

12 | Compactness and continuity | |

13 | Connectedness and connected spaces; connectedness of the subspaces; the connected subsets with respect to usual topology of reel numbers | |

14 | Connectedness and continuity |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assoc. Prof. Dr. Faruk POLAT |

Instructors | - |

Assistants | - |

Resources | Genel Topoloji (7. Baskı), Şaziye Yüksel, Eğitim Akademi Yayınları, 2011 |

Supplementary Book | Genel Topolojiye Giriş ve Çözümlü Alıştırmalar (3. Baskı), Mahmut Koçak, 2011 Topology (2nd Edition), James R. Munkres, Prentice Hall, Upper Saddle River, 2000 Basic Topology (Undergraduate Texts in Mathematics), M. A. Armstrong, Springer-Verlag, New York, 2010 Elementary Topology Problem Textbook, O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, American Mathematical Society, 2008 General Topology (Schaums`s Outline Series), Seymour Lipschutz, McGraw-Hill, 2011 A General Topology Workbook, Iain T. Adamson, Birkhauser, Boston, 1996 |

Document | - |

Goals | To introduce the notion of a topological space, to take notice that the reel spaces studied in analysis are the examples of topological spaces, and to show that many of the basic notios and properties in these spaces can be generalized to an arbitrary topological space |

Content | The notions of topology and open set, examples of topological spaces; The usual toplogy of reel numbers; The notion of neighborhood and the family of neighborhoods; The position of a point to a set; The interior, exterior, boundary, isolated points and the closure of a set; The basis and subbasis of a topology; The notion of continuity, continuity at a point and continuity on a space, the characteristics theorems of a continuity; Open and closed functions, homeomorphisms; The initial topology and product spaces; The final topology and quotient spaces; The subspaces, the inherited and topological properties; Compactness and compact spaces; Compactness and continuity; Connectedness and connected spaces; Connectedness and continuity |

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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