TOPOLOGY

Paper Code: 
MAT 222
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Unit I: 
I
15.00
Metric Spaces-Definition and examples, Open spheres and Closed spheres, Open sets and Closed sets, Neighbourhood, Sequence in metric space. Continuous mapping and Completeness in metric space.
 
Unit II: 
II
15.00
Topological Spaces-Definition and examples, Closed sets, Neighbourhood, Open base and sub base. Limit points, Adhere points and derived sets, Closure of a set, Subspaces, Continuity and Homeomorphism. 
 
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: To 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, General product spaces. 
 
Essential Readings: 
  1. George F. Simmons,2004, Introduction to Topology and Modern  Analysis,Mcgraw Hill Book Company.       
References: 
  1. Dugundji,J,Topology,Prentice Hall of  India,New Delhi,1975  
  2. Munkers R James, A first course in Topology,Pearson Education Pvt. Ltd.,Delhi        
 
Academic Year: