Akademik Dersler - Tanıtım


Code - Course Title	MAT326 - Metric and Topological Spaces II
Course Type	Required Courses
Language of Instruction	Türkçe
Laboratory + Practice	2+2
ECTS	5.0
Course Instructor(s)	PROFESÖR NEDİM DEĞİRMENCİ
Mode of Delivery	The mode of delivery of this course is Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	It is suggested to take Abstarct Algebra, Analytic Geometry and Analysis courses.
Recommended Reading List	1.Karaçay,T; Genel Topoloji; Başkent Üniversitesi2.W.A.Sutherland; Metrik ve topolojik uzaylar; Anadolu Üni.Yay.(çeviri)3. Bülbül.A; Genel Topoloji, Hacettepe Üni.yay.
Assessment methods and criteria	2 midterms, 1 final.
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	Compactness of topological spaces, Compact spaces and compactness of subspaces
Week - 2	Compactness of topological spaces; Some relations among compactness, closed sets and continuous functions
Week - 3	Compactness of topological spaces; Compactness of product spaces, some examples
Week - 4	Compactness of topological spaces; Countably compact and sequentially compact spaces
Week - 5	Compactness of topological spaces; Locally compact spaces, compactness and completeness in metric spaces
Week - 6	Connectedness; Connected spaces and connected subsets
Week - 7	Connectedness; connectedness and continuous functions, connectedness of product spaces
Week - 8	Connectedness; Path-connected spaces, components, locally connected spaces
Week - 9	Connectedness; Disconnected and totally disconnected spaces
Week - 10	Complete Metric Spaces: Completeness concept
Week - 11	Complete Metric Spaces: Fixed point theorems
Week - 12	Complete Metric Spaces: Contraction theorems
Week - 13	Arzela-Ascoli theorems
Week - 14	Completion of metric spaces

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
1.Midterm Exam	1	20
2.Midterm Exam	1	30
Final Exam	1	50
Toplam (%)		100