NAMEPRACTICAL/TUTORIAL GROUP
Unit Course book
General Topology
Course code:MthP 411 GTO
Unit Coordinator
Dr. Wadhah S. Jassim
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 4
Soran University
Faculty of Science
Department of Mathematics
Course Book
General Topology
Fourth Year Mathematics department
Academic Year 2012 - 2013
Three Hours Per Week
Lecturer: Dr. Wadhah S. Jassim
Assistant Professor in Mathematics - Algebra
e- mail: wadhahjassim@yahoo.co.uk
M: o7702584067
1
Soran University
Faculty of Science
Department of Mathematics
Course Book
General Topology
Fourth Year Mathematics Department
Academic Year 2012 - 2013
Three Hours Per Week
Lecturer: Dr. Wadhah S. Jassim
Assistant Professor in Mathematics - Algebra
e- mail: wadhahjassim@yahoo.co.uk
M: o7702584067
Office hours: Sunday – Tuesday
9am – 3 Pm
Classes :
Sunday : 8.30 am – 11.30 am
11.30 am – 12.30 pm
Tuesday: 8.30 am – 10.30 am
10.30 am – 12.30pm
2
Course Objective
The course provide a mathematically rigorous introduction to metric spaces, Topological spaces, product topology, Connected spaces, compact spaces, Separation axioms and complete metric topology. I have followed the principle that the material should be as clear and as intuitive as possible. A major aim of this course is to teach students to understand the concepts and the methods of proving of topological spaces, Connectedness, Compactness and separation.
Methods of teaching
Different methods of teaching will be used to reach the aim of this course, such as the attention given to motivating the ideas under discussion, work sheet will be designed to let the chance for practicing on several aspects of the course in the class room. Also power point will be used .
Grading
The students are required to do two closed book exam at each term . The midterm exam has 15 marks, the attendance, class room activities and quizzes count 5 marks . Therefore the total mark for the first term is 20 marks and similarly for the second term. Therefore midterms exams count 40 marks and the final exam has 60 marks. Hence the grade will be best up on the following criteria :
Midterm exams : 30%
Class room participation and assignments : 10 %
Final exam : 60 %.
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Marking System
The grades for each piece of assessed work are as follows:
90 – 100 % excellent
80 – 89 % Very good
70 – 79 % good
60 – 69 % moderate pass
50 – 59 % Pass
49 < % Fail
Course Programme
Weeks 1: Introduction to metric spaces. Definition of metric
space, examples, distance between two subsets of
metric spaces, distance between a point and a
subset of metric spaces and the diameter of a
subset of metric space.
Week 2: Open Spheres, open sets, Limits points, Closed sphere, closed
sets in metric spaces . Continuous functions of metric spaces.
Week 3 : Topological space
Definition of topological space, examples, Open sets
and closed sets in a topological space.
Week 4: Closure sets , Interior sets and its properties.
Week 5: First Exam
Week 6: Exterior sets , dense , neighborhood of a point and its
properties.
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Week 7: Bases of topological spaces . Definitions and theorems
Week 8: finer and coarser , equivalent bases
Week 9: Open Neighborhood system, subbases . Definitions and
theorems.
Week 10: Second exam
Week 11: First Term holiday
Week 12 : Continuous functions of Topological spaces
Week 13 : Definitions, Theorems and properties
Week 14 : Homeomorphisms of topological spaces.
Week 15: Third Exam
Weeks 16, 17,18 and 19: Training of teaching.
Week 20 : Compact spaces, covers , open cover, subcover .
Week 21 : finite cover and its properties.
Week 22: Connected spaces and its properties.
Week 23: Fourth Exam
Week 24: T0 - space, T1 – space and T2 - space.
Week 25 : Product topologies, Regular space and normal space.
Week 26 : Quotient spaces and Metrization.
References
1) C. Wayne Patty ;" Foundations of Topology", second Edition, 2009.
2) G. F. Simmons; " Introduction To Topology and Modern Analysis",
International Student Edition.
3) M. C. Gemignani; " Elementary Topology" , Second Edition,1972,
4) W. J. Pervin; " Foundations of General Topology",