Information
Code | MT503 |
Name | General Topology |
Term | 2024-2025 Academic Year |
Semester | . Semester |
Duration (T+A) | 3-0 (T-A) (17 Week) |
ECTS | 6 ECTS |
National Credit | 3 National Credit |
Teaching Language | Türkçe |
Level | Yüksek Lisans Dersi |
Type | Normal |
Mode of study | Yüz Yüze Öğretim |
Catalog Information Coordinator | Prof. Dr. ALİ ARSLAN ÖZKURT |
Course Goal / Objective
The aim of this course to provide information about countability in topological spaces, product spaces, weak topologies, embedding, homeomorphism, convergence, separation axioms and compactness .
Course Content
Countability in topological spaces, product spaces, embedding theorems, convergence, separation axioms, compactness,
Course Precondition
Pre-requisites None
Resources
S. Willard : General Topology
Notes
J. Dgundji : General Topology
Course Learning Outcomes
Order | Course Learning Outcomes |
---|---|
LO01 | Defines first and second countable spaces |
LO02 | Comprehends Product topology, weak topology and embedding theorems |
LO03 | Understands convergence of a sequence, the net and filter in topological spaces, |
LO04 | Establishes a relationship between convergence in analysis and topology. |
LO05 | Can define Hausdorff, regular and normal spaces |
LO06 | Understands the compact space and comprehends basic theorems about compact spaces. |
LO07 | Understands the relationship between compactness and convergence. |
LO08 | Improves the ability of abstract thinking. |
Relation with Program Learning Outcome
Order | Type | Program Learning Outcomes | Level |
---|---|---|---|
PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 3 |
PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 3 |
PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 4 |
PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 3 |
PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 3 |
PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 4 |
PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | |
PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 4 |
PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 4 |
Week Plan
Week | Topic | Preparation | Methods |
---|---|---|---|
1 | Review of some topological concepts. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
2 | Sub-base and the concept of neighborhood. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
3 | Sub-base and the concept of neighborhood 2 | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
4 | First and Second countable spaces | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
5 | Product spaces and weak topologies | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
6 | Separable spaces and Embedding Theorems. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
7 | Convergence of sequences, Sequential continuity | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
8 | Mid-Term Exam | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
9 | Nets and Convergence. Filters and convergence. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
10 | T0 and T1-spaces. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
11 | T2 (Hausdorff), regular, T3-spaces. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
12 | Completely regular, normal spaces and Jone's Lemma. and T4-spaces. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
13 | Tychonoff spaces and T4 spaces | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
14 | The compactness andthe finite intersection property, and the relationship between the compactness and convergence. Heine-Borel Theorem. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
15 | Fundamental properties of compact spaces and Heine-Borel Theorem. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
16 | Term Exams | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
17 | Term Exams | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
Works | Number | Time (Hour) | Workload (Hour) |
---|---|---|---|
Course Related Works | |||
Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
Assesment Related Works | |||
Homeworks, Projects, Others | 0 | 0 | 0 |
Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
Final Exam | 1 | 30 | 30 |
Total Workload (Hour) | 157 | ||
Total Workload / 25 (h) | 6,28 | ||
ECTS | 6 ECTS |