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TOPOLOGY [1]

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

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.

15.00

Compact and Locally Compact spaces, Connected and Locally connected spaces, Continuity and Compactness, Continuity and Connectedness.

15.00

Separation axioms: To space, T1 space, T2 space or Hausdroff space, Regular and T3 spaces, Normal and T4 spaces.

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

         2. 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      

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