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 about the need of the topology in Mathematics.

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Paper Code

Paper 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 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

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Team teaching

 

Learning activities for the students:

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

Class test, Semester end examinations, Quiz, 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., 1983.
  • 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.
  • 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, 1983.
 
Academic Year: 
2021-2022
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