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Topology and Introduction to Functional Analysis

Objectives

The aim of the course is to provide the student with the concepts, methods and elementary techniques of GeneralTopology and Functional Analysis. The course provides the foundations of the most advanced theory of normed spaces, Banach spaces, and Hilbert spaces, and despite the special emphasis on normed linear spaces (ofarbitrary dimension), structural and fundamental results are established in general topological spaces, essentials for the student who wishes to pursue advanced studies in mathematics.

General characterization

Code

12916

Credits

9.0

Responsible teacher

Oleksiy Karlovych

Hours

Weekly - 4

Total - 56

Teaching language

Português

Prerequisites

Knowledge in Linear Algebra and Mathematical Analysis.

Bibliography

 1. Bollobás, B. (1990),  Linear Analysis, an Introductory Course, Cambridge University Press.

2.    Kreyszig, E. (1978), Introductory Functional Analysis with Applications,  New York: John Wiley&Sons.

3.  Lima, E. L. (1970), Elementos de Topologia Geral, Ao Livro Técnico, Editora da Universidade de São Paulo.

4. Sutherland, W. A. (2009), Introduction to Metric and Topological Spaces, Oxford University Press.

Teaching method

Available soon

Evaluation method

Available soon

Subject matter

1. Introduction to the TIAF Course

  Metric spaces

2. Linear normed spaces

3. Bounded linear operators on linear normed spaces

4. Banach spaces

5. Inner product spaces. Hilbert spaces

6. Fundamental theorems for normed linear spaces

7. Topological spaces

8. Connection in topological spaces