Topology

Paper Code: 
24DMAT802
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to

  1. Understand the concept of fundamentals of point set topology. 
  2. Describe different topological spaces.
  3. Aware about the need of the topology in Mathematics.

 

Course Outcomes: 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 24DMAT

802

 

 

 

 

 

 

 

 

Topology

(Theory)

 

CO118: Analyze properties of topological spaces and construct various topologies on a general set.

CO119: Explain continuous functions, Homeomorphisms, Net and filters to understand structure of topological spaces.

CO120: Outline the concept of compactness and connectedness

CO121: Categorize the separation axioms and produce examples for different topological spaces.

CO122: Explore the concept of product spaces and quotient spaces.

CO123: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Tutorials

 

Learning activities for the students:

Self learning assignments, Effective questions, Presentation, Assigned tasks.

 

 

Quiz,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

Unit I: 
Topological Spaces:
18.00

 Definition and examples, Closed sets, Neighborhood, Open base and sub base, Limit points, Adhere points and derived sets, Closure of a set.

 

Unit II: 
Subspaces, Continuity and Nets and Filters:
18.00

Subspaces, Continuity and homeomorphism, Nets, Filters and related theorems.                                                                                                                                                                                                                                                                                                                       

 

Unit III: 
Compactness and Connectedness:
18.00

Compact and locally compact spaces, Connected and locally connected spaces, Continuity and compactness, Continuity and connectedness.

 

Unit IV: 
Separation axioms:
18.00

T0 space, T1 space, T2 space of Hausdorff space, Regular and T3 spaces, Normal and T4 spaces.

 

Unit V: 
Product spaces:
18.00

Product space of two spaces, Product invariant properties for finite products, Quotient spaces.

 

Essential Readings: 
  • George F. Simmons, Introduction to Topology and Modern Analysis, McGraw Hill, 2004.
  • Colin Adams and Robert Franzosa, Introduction to Topology, Pearson’s united edition press, 2007.
  • K. D. Joshi, Introduction to General Topology, Wiley Eastern Ltd., 1985.
  • J. Dugundji., Topology, Prentice Hall of India, New Delhi, 1975.
  • Munkers R James, A first Course in Topology, Pearson Education Pvt. Ltd., Delhi, 2015.
  • Terry Lawson, Topology: A Geometric Approach, Oxford University press, 2003.

 

References: 
  • John L. Kelley, General Topology, Dover Publications; Reprint edition, 2017
  • Stephen Willard, General Topology, Wesley Publishing Company, Reading, Massachusetts, 1970.
  • Tej Bahadur Singh, Introduction to Topology, Springer Singapore, 2019.
  • W.J. Pervn, Foundation of General Topology, Academic Press Ltd., 1996.
  • M.G. Murdeshevar, Topology, Wiley Eastern Ltd, 1986.

e- RESOURCES

JOURNALS

 

Academic Year: 
2024-2025
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