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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
TOPOLOGY II	801500715040		3 + 0	3.0	8.0

Prerequisites

None

Language of Instruction	Turkish
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery	Oral presentation, answer-question, discussion, solving problems.
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Goals	This lecture starts with an elementary study of the extended real line, and, deals with properties of finite numerical functions which result from the fact that real line is a field and an ordered set, and certain classes of finite numerical functions and numerical functions (the mappings on an arbitrary set into the extended real line).
Course Content	Topology of the Line Line R and ¯R.Numerical functions defined on an arbitrary set, bounds of numerical functions, upper and lower envelopes of a family of functions, limit superior and inferior of a function along a filter base. Continuity, semicontinuity, lower and upper semicontinuous functions, monotone functions. Convex functions, continuity and differentiability of convex functions, criteria for convexity, convex functions on a subset of a vector space.
Learning Outcomes	1) Learns the extended real line. 2) Learns the properties of real valued and extended real valued functions. 3) Learns to find the limit superior and inferior of a function along a filter base. 4) Learns the lower and upper semicontinuity. 5) Learns the Stone-Weierstrass Theorem. 6) Learns the properties of convex functions.