FUNKCIONALNA ANALIZA

On successful completion of the course, students will be able to: 1. Explain the concepts and present some examples of metric spaces, topological spaces, normed spaces. They will also be able to define the convergence in a topological space, and explain the concept of complete metric space and basic theorems of metric spaces (Banach fixed point theorem, Baire’s category theorem, Cantor’s intersection theorem). 2. Explain the concept of the linear operator and operator norm. Understand the possibility of application of these concepts and theorems to prove the convergence of numerical methods for solving systems of linear equations. 3. Formulate and prove Hahn-Banach theorem and geometric Hahn-Banach theorem (hyperplane separation theorem). 4. Understand why certain theorems of functional analysis are particularly important (fundamental). 5. Read scientific papers, monographs and reference literature that use concepts and methods of functional analysis.