Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Analysis

Code

lehalm1u0um17em

Title

Descriptive set theory (l)

Usual semester

Spring

Published semester

2025/26/2

ECTS

4

Language

en

Learning outcomes

Knowledge: Knowledge of basic concepts, results and methods in the field. Ability: Application of knowledge in the field, understanding of interrelationships and problem solving. Attitude: Desire to improve mathematical knowledge and to learn as much as possible, and to apply knowledge as widely as possible. Autonomy and responsibility: Formulate and analyse mathematical questions independently and evaluate the limits of their applicability responsibly.

Course content

Polish spaces. The Category Theorem and its applications. Typical (generic) continuous functions. The Baire property. The Kuratowski–Ulam Theorem. Transfinite classes of Borel sets. The Baire classes of functions. The Suslin operation. Analytic and coanalytic sets. Projective sets. The method of finer topologies. Infinite games, their determinacy, and their applications. Connections with set theory.

Assessment method

oral exam and grade for the problem solving class

Bibliography

lecture notes

Recommended bibliography

A. S. Kechris: Classical descriptive set theory, Springer, 1998. Laczkovich Miklós:  Valós függvénytan (egyetemi jegyzet), ELTE Budapest, 1995.

Programmes of the course