Akademik Dersler - Tanıtım


Code - Course Title	MAT3010 - Metric and Topological Spaces II
Course Type	Required Courses
Language of Instruction	Türkçe
Laboratory + Practice	4+0
ECTS	5.0
Course Instructor(s)	PROFESÖR DOKTOR MUSTAFA SALTAN
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.
Required or Recommended Resources	Metrik ve Topolojik Uzaylara Giriş, Sutherland, W.A. (Çeviri) Anadolu Üniv. Yayınları, (1997).Introduction to Metric and Toplogical Spaces, Sutherland,W.A. (1997).Metric Spaces, Micheal Searchoid, Springer, (2007).
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	Subspaces; subspaces of the standard space R^n.
Week - 2	Continuous functions in topological spaces; continuity theorems.
Week - 3	Interior, exterior, closure, and boundary of a set in topological spaces.
Week - 4	Bases and subbases of a topology; second countable spaces.
Week - 5	Product spaces.
Week - 6	Separation axioms; Hausdorff spaces; T0-spaces, T-1 spaces.
Week - 7	Homeomorphisms; topologically equivalent spaces.
Week - 8	Hereditary properties; topological properties.
Week - 9	Quotient spaces.
Week - 10	Connected spaces.
Week - 11	Connected components; path-connected spaces.
Week - 12	Compactness in topological spaces.
Week - 13	Heine–Borel Theorem and some applications.
Week - 14	Relationships between compactness and sequential compactness.

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
Toplam (%)		0