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.
Unit II:
II
9.00
Continuous mappings, Sequence in a Metric Space, Cauchy Sequence, Subsequence, Completeness of Metric Space.
Unit III:
III
9.00
Separable Space, Compact spaces and Compact Sets, Connected Spaces and Connected Sets, Bolzano’s Theorem, Product Spaces.
Unit IV:
IV
9.00
Vector space: Definition with Examples, Sub-space, Linear combination of vectors, Linear Span.
Unit V:
V
9.00
Linearly dependent and independent vectors and their simple properties, Bases and dimension.
Essential Readings:
K. C. Sarangi, Real Analysis and Metric Space, RBD, Jaipur.
P.B.Bhattacharya , S.K.Jain and S.R.Nagpaul,Basic Abstract Algebra , Cambridge University Press.
G. C. Sharma , Modern Algebra, Shivlal Agarwal & Co. Agra.
