Introduction, Metric space, subspace, Triangle inequality,
Axioms of a metric, Sequence space, Space B(A) of bounded functions, Some Inequalities, Ball and sphere, Continnous mapping,
accumulation point, Dense set, separable space, Convergence of a sequence,
limit, Cauchy sequence, completeness,
Real line, complex plane, Uniform convergence, Discrete metric, Isometric
mapping, isometric spaces, Homeomorphism, Normed Space, Banach Space, Further Properties of Normed Spaces,
Finite Dimensional Normed Spaces and Subspaces, Compactness and Finite
Dimension, Linear Operators,
Bounded and Continuous Linear Operators, Linear Functional, Linear Operators
and Functional onFinite
Dimensional Spaces, Normed Spaces of Operators, Dual Space, Inner Product Space,
Hilbert Space, Further Properties of Inner Product Spaces, Orthogonal Complements and Direct Sums, Orthonormal
Sets and Sequences,
Series Related to Orthonormal Sequences and Sets, Total Orthonormal Sets and
Sequences, Legendre Hermite and Laguerre Polynomials, Representation of Functional on
Hilbert Spaces, Hilbert Adjoint
Operator, Self-Adjoint, Unitary and Normal Operators.