MT559 Topics in General Topology I

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

Information
Goal, Content & Resources
Course Learning Outcomes
Relation with Program Learning Outcome
Week Plan
Student Workload - ECTS

Information

Code MT559
Name Topics in General Topology I
Semester . Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 6 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Doktora Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. ALİ ARSLAN ÖZKURT


Course Goal

To teach Some advenced topics in General Topology

Course Content

Local Compactness, Paracompactness, Metrization Theorems, Connectedness and Uniform spaces

Course Precondition

Pre-requisites None

Resources

J. Dgundji: General topology

Notes

Lecture Notes


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Knows the properties of locally compact spaces
LO02 Knows the paracompact spaces and their properties
LO03 Knows Urysohn Metrization Theorem
LO04 Knows Nagata-Smirnov Metrization Theorem
LO05 Knows Baire-Category Theorem
LO06 Knows connected,,pathwise connected, arc-wise connected,locally connected, locally path connected, locally arc-wise connected spaces and their properties
LO07 Knows uniformity and the concept of uniform spaces


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Knows the results of previous research in a special field of mathematics 5
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in her 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. 4
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics 3
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 3
PLO07 Bilgi - Kuramsal, Olgusal Sets up original problems in her field and offers different solution techniques 4
PLO08 Bilgi - Kuramsal, Olgusal It carries out original and qualified scientific studies on the subject related to its field.
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories.
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 foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. 3
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. 3
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 5


Week Plan

Week Topic Preparation Methods
1 locally compact spaces and some properties Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
2 Paracompact spaces and some properties Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
3 Metrizable spacesi Lebesque covering lemma Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
4 Urysohn Metrization Theorem Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
5 Urysohn Metrization Theorem 2 Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
6 Nagata-Smirnov Metrization Theorem Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
7 Baire- Category Theorem 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:
Ödev
9 connected spaces and properties Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
10 pathwise and local connectedness Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
11 Continuun and Properties of metric continuum Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
12 Totally disconnected spaces Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
13 Cantor Set and Peano spaces Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
14 Uniform Structures and Uniform spaces Read the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
15 Uniform Structures and Uniform spaces 2 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:
Ödev, Performans Değerlendirmesi
17 Term Exams Topics discussed in the lecture notes and sources again Ölçme Yöntemleri:
Ödev, Performans Değerlendirmesi


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