Topology

Paper Code: 
MAT222
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to

  1. Understand the concept of fundamentals of point-set topology.  
  2. Understand the introduction to topological spaces.
  3. Aware of the need for the topology in Mathematics.

 

Course Outcomes (COs):

course learning learning

Learning outcomes

(at course level)

Learning and teaching strategies assessment

Assessment

Strategies

Course Code

Course Title

MAT 222

 

Topology

(Theory)

 

The students will be able to –

 

CO42: Analyze properties of topological spaces and construct various topologies on a general set.

CO43: Use continuous functions, homeomorphisms, net, and filters to understand the structure of
topological spaces.

CO44: Correlate the concept of continuity to compact and connected spaces.

CO45: Categorize the separation axioms and produce examples for different topological spaces.

CO46: Understand the concept of product spaces and quotient spaces.

CO47: Apply the topological concepts and constructions to some chosen real-world problems

 

The approach in teaching:

Interactive Lectures, Discussions, Tutorials, Team teaching

 

Learning activities for the students:

Self-learning assignments, Effective questions, Topic  presentation, Giving tasks, 

Class test, Semester end examinations, quizzes, Presentation

 

Unit I: 
I
15.00
Topological Spaces: Definition and examples, Closed sets, Neighborhood, Open base and sub base, Limit points, Adhere points and derived sets, Closure of a set.
 
Unit II: 
II
15.00

Subspaces, Continuity and homeomorphism, Nets, Filters.

Unit III: 
III
15.00
Compact and locally compact spaces Connected and locally connected spaces, Continuity and compactness, Continuity and connectedness.
 
Unit IV: 
IV
15.00
Separation axioms: T0 space, T1 space, T2 space or Hausdroff space, Regular and T3 spaces, Normal and T4 spaces.
 
Unit V: 
V
15.00
Product spaces: 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, Pearsons united edition press, 2007.
  • K.D. Joshi, Introduction to General Topology, Wiley Eastern Ltd., 1985.
  • Dugundji. J, 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.
 
Academic Year: 
2022-2023
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