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MATH
402
Topology
II
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Instructor:
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Assoc. Prof.
Dr. Murat Adývar
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Office:
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Room: 424
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Office
Hours:
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Friday 12:30-14:30 (or by appointment)
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e-Mail:
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murat.adivar@ieu.edu.tr
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Phone:
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(232)
488-8377
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Class Hours:
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Monday 12:30-15:20 Classroom: M 105
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Announcements:
Announcements will be given in class and posted to the course
web site. Students should
regularly check the web site for new and updated
announcements.
Objectives:
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Topology is a natural, geometric, and intuitively appealing branch of mathematics which can be effective vehicle to understand advanced mathematical topics. The second-tier of this course is designed to cover the usual
topics of point set topology such as Metric spaces, connectedness, compactness, metrization, e.t.c.
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Course Outline:
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1
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Metric Spaces: Open sets and closed sets in metric spaces, Interior closure and boundary
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2
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Cauchy sequences and completeness of metric spaces
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3
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Continuity on metric space and Uniform continuity
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4
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Connectedness: Connected and disconnected
spaces
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5
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Theorems on connectedness, connected subsets of the Real line
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6
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Path connected spaces
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7
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Locally connected and locally path connected spaces
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8
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Compactness: Compact spaces and subspaces, Compactness and continuity
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9
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Properties related to compactness
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10
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Limit point
compactness, sequentially
compactness
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11
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One point compactification,
Local compactness
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12
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Seperation properties and metrization: T_0,
T_1 and T_2 spaces
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13
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Regular spaces and
Normal spaces, Seperation
by continuous functions
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14
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Metrization, The Stone-Čech compactification
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Textbook:
James R. Munkres,
Topology, Prentice Hall, ISBN 0-13-181629-2
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References:
Fred H. Croom,
Principles of Topology, The Saunders Series, ISBN
0-03-012813-7
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Articles:
Will
be handed out in class as needed.
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Assignments:
Homework
and reading assignments will be given in class.
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Evaluation:
Students
will receive a final letter grade according to the scale shown below,
formulated with the percentages in the below table. Performance shown in
homework, quizzes, exams and participation make up an important part of
instructor's final opinion.
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Grading
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Percent
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Midterm
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40
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Final
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40
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Homeworks
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10
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Quizzes
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10
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Multipliers and 100-point score equivalents of Letter Grades are
shown below:
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Score
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Semester Grade
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Mult.
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90-100
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AA
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4.0
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85-89
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BA
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3.5
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80-84
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BB
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3.0
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75-79
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CB
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2.5
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70-74
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CC
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2.0
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65-69
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DC
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1.5
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60-64
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DD
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1.0
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50-59
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FD
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0.5
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49 and
below
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FF
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0.0
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Attendence:
Attendance is required at all times. Students are
expected to come to class fully prepared to discuss textbook readings and
course assignments.
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