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METRIC AND VECTOR SPACE [1]

Paper Code: 
MAT602
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
9.00

Metric Space: Definition with examples, Bounded set, Open set, Closed sets, Neighbourhoods Boundary points and limit points, Exterior point, Closure of a set, Metric Subspace.
 

9.00

Continuous mappings, Sequence in a Metric Space, Cauchy Sequence, Subsequence, Completeness of Metric Space.

 

9.00

Separable Space, Compact spaces and Compact Sets, Connected Spaces and Connected Sets, Bolzano’s Theorem, Product Spaces.
 

9.00

Vector space: Definition with Examples, Sub-space, Linear combination of vectors, Linear Span.
 

9.00

Linearly dependent and independent vectors and their simple properties, Bases and dimension.

 

Essential Readings: 
  1. Real Analysis and Metric Space, K. C. Sarangi, RBD, Jaipur.
  2. Basic Abstract Algebra, P.B.Bhattacharya , S.K.Jain and S.R.Nagpaul,Basic Cambridge University Press.
  3. Modern Algebra, G. C. Sharma, Shivlal Agarwal & Co. Agra.
     
References: 
  1. Abstract Algebra, Deepak Chatterjee, PHI. Ltd. New Delhi.
  2. Topics in Algebra, I.N. Herstein, Wiley Eastern Ltd., New Delhi

 

Academic Year: 
2017-2018 [2]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/metric-and-vector-space-1

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/metric-and-vector-space-1
[2] https://maths.iisuniv.ac.in/academic-year/2017-2018