METRIC AND VECTOR SPACE

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