Syllabus
Spaces: metric, linear, normed, Banach, Hilbert.
Neighborhoods, closed and opens sets. Convergence in metric space, Bolzano-Cauchy condition, completeness.
Scalar product. orthogonality.
Linear functionals, Hahn-Banach theorem. Adjoint space. Linear operators.
Annotation
Main types of topological spaces will be introduced. Linear functionals andoperators will be defined and their fundamental properties will be studied.