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MATH
401
Topology
I
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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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Tuesday 14:30-17:30 (or by appointment via e-mail)
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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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Tuesday 11:30-14:20
Classroom: C 106
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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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This course covers the fundamentals of point set topology, starting from axioms of set algebra that will be useful to define a topological space. Topics typically include: Open and closed subsets, closure and interior of a set, topological spaces; the product topology, the quotient topology, e.t.c.
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Course Outline:
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1
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Introduction and fundamental
concepts of set theory
and logic
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2
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Indexed family of elements and family subsets
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3
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Countable and uncountable
sets, Infinite sets and the Axiom of Choice
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4
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Topological spaces
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5
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Open and closed
subsets of topological
spaces
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6
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Closure, interior and boundary of sets. Limit points
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7
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Continuous maps and
their properties
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8
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Subspace and the
subspace topology
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9
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Metric spaces and
metric topology
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10
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Hausdorff spaces
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11
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Homeomorphisms
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12
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The product topology
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13
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The order topology
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14
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The quotient topology
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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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