MATH-6203               Topology

DESCRIPTION 

A topology is basically a way to organize the network. The physical topology is the way you physically lay out the network, like a map, and the logical topology is the way the information flows on the network. Usually, the physical and logical topology is the same, but sometimes they can differ, such as in a physical star/logical ring topology.

LEARNING OUTCOMES

After the completion of the course, students will be able to

1. Understand the concept of Topology and can construct examples. 
2. Learn the properties certain concepts of Topology. 
3. Construct rigorous mathematical proofs of basic results in Topology.
4. Learn about the various kinds of Topological spaces.  

Contents

1. Topological spaces,
2. Bases and sub-bases,
3. First and second axiom of countability,
4. Separability,
5. Continuous functions and homeomorphism,
6. Finite product space,
7. Separation axioms  (T0, T1, T2),
8. Techonoff space,
9. Regular spaces,
10. Completely regular spaces,
11. Normal spaces,
12. Compact spaces,
13. Connected spaces.

Recommended Books

1. Lipschutz, S., General Topology, Schaum’s outline series, (McGraw Hill, 1968).
2. Sheldon, W.D., Topology, 1st ed. (McGraw Hill, 2005).

Suggested Books

1. Simon, G.F., Introduction to Topology and Modern Analysis,1st ed. ( McGraw Hill, 1963)
2. Willard,J., General Topology, 1st ed. (Addison-Wesley, 1970).
3. Munkers, J.R., Topology, 2nded. (Pearson Prentice Hall, 2006).

       Assessment Criteria

           Sessional: 20 (Presentation / Assignment 04, Attendance 08, Result Mid-Term 04, Quiz 04)

           Mid-Term Exam:  30

           Final-Term Exam: 50

Key Dates and Time of Class Meeting

MSc Mathematics (Regular)                   

Tuesday: 09:30 AM-11:00 AM,         

Friday: 09:30-11:00 AM

Commencement of Classes                                                    October 26, 2020

Mid Term Examination                                                             December 28, 2020

Final Term Examination                                                           March 01-05, 2021

Declaration of Result                                                               March 12, 2021