| Course Description : | Metric spaces, examples of metric spaces, open sets, closed sets, neighbourhoods, convergence, Cauchy sequences, completeness, examples of complete metric spaces, completion of metric spaces,
vector spaces, infinite dimensional vector spaces and subspaces, linearly dependent and independent vectors, Hamel basis, normed spaces, Banach spaces, properties of normed spaces, compactness and finite dimensional spaces, linear functionals, dual spaces, inner product spaces, Hilbert spaces, orthonormal sets and sequences, linear operators, bounded and continuous linear operators. |