MT503 General Topology

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

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

Update Time: 25.06.2024 10:09