Courses

Supremum, infimum, limsup, liminf. Cauchy completeness of real numbers, completeness with respect to order, Archimedean property. Series, ratio and root criteria regarding limsup, liminf. Condensation criteria, Raabe. Alternating series, rearrangements, products. Topology of R2 and R3. Convergence and continuity of functions of several variables. The concept of metric space. Metrics on Rn, Holder - Minkowski inequalities. Open and closed sets, interior and case. Continuous functions. Complete metric spaces, boxed, Cantor theorem. Fixed point theorem. Applications: Picard theorem, entangled function theorem. Information: Renaming of the Course "Real Analysis IV" in the Academic Year 2020-21.