Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | FMA604 | TOPOLOGY II | Compulsory | 1 | 2 | 6 |
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Level of Course Unit |
Second Cycle |
Objectives of the Course |
The aim of the course is
• to gain the basic information necessary in the field of topology.
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Name of Lecturer(s) |
Yrd. Doç. Dr. Serkan KARATAŞ |
Learning Outcomes |
1 | To have the ability and knowledge of the advanced level of related to the field and use it in a real learning environment. |
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Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
• Identical topology and Quotient Space: Identical topology and Identical Function (or Identical)
• Characteristics features of Identification
• Quotient Space and Canonical Function
• Saturated sentences in the equivalence connected topological space and the closure and the Interior and the complement of saturated sentence
• Paracompact spaces: Local Finite Family
• Features of local finite sub-sentences family
• Paracompactness of a compact space
• A paracompact space which is being a Normal space View of a Paracompact space under continuous and closed functions
• Paracompactness of Metric spaces
• Filters: Filters Comparison
• Basis of filter
• Ultra filter
• Necessary and sufficient condition for being ultra filter of a filter
• Image and Inverse Image of a filter
• Convergence of a filter
• Continuous image of a convergent filter
• The filter characterization of Compact Spaces
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Weekly Detailed Course Contents |
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1 | Identical topology and Quotient Space: Identical topology and Identical Function (or Identical)
| | | 2 | Characteristics features of Identification
| | | 3 | Quotient Space and Canonical Function
| | | 4 | Saturated sentences in the equivalence connected topological space and the closure and the Interior and the complement of saturated sentence
| | | 5 | Saturated sentences in the equivalence connected topological space and the closure and the Interior and the complement of saturated sentence
| | | 6 | Paracompact spaces: Local Finite Family, Features of local finite sub-sentences family
| | | 7 | Paracompactness of a compact space
| | | 8 | Midterm exam
| | | 9 | A paracompact space which is being a Normal space
| | | 10 | View of a Paracompact space under continuous and closed functions
| | | 11 | Paracompactness of Metric spaces
| | | 12 | Filters: Filters Comparison, Basis of filter, ultra fitler
| | | 13 | Necessary and sufficient condition for being ultra filter of a filter
| | | 14 | Image and Inverse Image of a filter, Convergence of a filter
| | | 15 | Continuous image of a convergent filter, the filter characterization of Compact Spaces
| | | 16 | Final exam
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Recommended or Required Reading |
Munkres, James R. 2000;Topology. Second edition, Prentice-Hall Inc.,Englewood Cliffs, N.J., |
Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
SUM | 0 | |
SUM | 0 | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | SUM | 100 |
| Language of Instruction | Turkish | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 2 | 2 |
Final Examination | 1 | 2 | 2 |
Makeup Examination | 1 | 2 | 2 |
Attending Lectures | 14 | 6 | 84 |
Problem Solving | 10 | 3 | 30 |
Self Study | 14 | 4 | 56 |
Individual Study for Mid term Examination | 10 | 4 | 40 |
Individual Study for Final Examination | 8 | 4 | 32 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Ordu University Rectorate Building ,Cumhuriyet Campus , Center / ORDU / TURKEY • Tel: +90 452 226 52 00
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