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Topology [1]

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

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.

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.

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

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

Product spaces: Product space of two spaces, Product invariant properties for finite products, General product spaces.

Essential Readings: 
  1. George F. Simmons, Introduction to Topology and Modern Analysis, Mcgraw Hill Book Company(2004).   
  2. Colin Adams [2], Robert Franzosa [3], Introduction to Topology, parsons united   edition press (2007).

    

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
  3. Terry Lawson, Topology: A Geometric Approach [4], Oxford University press (2003).
Academic Year: 
2016-2017 [5]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/topology-1

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/topology-1
[2] http://www.pearsoned.co.uk/bookshop/Results.asp?iCurPage=1&Type=1&Author=Colin+Adams&Download=1&SearchTerm=Colin+Adams
[3] http://www.pearsoned.co.uk/bookshop/Results.asp?iCurPage=1&Type=1&Author=+Robert+Franzosa&Download=1&SearchTerm=+Robert+Franzosa
[4] https://global.oup.com/academic/product/topology-a-geometric-approach-9780198515975?prevSortField=1&sortField=1&start=20&resultsPerPage=20&prevNumResPerPage=20&lang=en&cc=in
[5] https://maths.iisuniv.ac.in/academic-year/2016-2017