Subjects(version: 944)
Descriptive Set Theory 2 - NMMA434
Title: Deskriptivní teorie množin 2 Department of Mathematical Analysis (32-KMA) Faculty of Mathematics and Physics from 2023 summer 4 summer s.:2/0, Ex [HT] unlimited unlimited no no taught Czech, English full-time full-time
Guarantor: RNDr. Václav Vlasák, Ph.D. M Mgr. MAM Mgr. MA > Povinně volitelné Mathematics > Real and Complex Analysis NRFA072 NRFA072 NRFA072
 Annotation - ---CzechEnglish
Last update: T_KMA (02.05.2013)
Advanced topics in the clasical descriptive set theorey. Continuation of NMMA433. Recommended for master students of mathematical analysis.
 Literature - Czech
Last update: T_KMA (02.05.2013)

KECHRIS A.S. Classical Descriptive Set Theory, Graduate Texts in Mathematics 156, Springer, 1995.

 Requirements to the exam - Czech
Last update: doc. Mgr. Benjamin Vejnar, Ph.D. (31.01.2022)

Zkouška má ústní formu s písemnou přípravou. Studentovi bude zadáno téma, ke kterému si připraví související věty, definice a důkazy.

 Syllabus - ---CzechEnglish
Last update: RNDr. Václav Vlasák, Ph.D. (09.05.2018)

1. Analytic sets and trees: Suslin sets and Suslin operation, Suslin operation and space of trees, Luzin-Sierpinsky index and coanalytic norms, Luzin separation theorems and principle of reduction.

2. Measurable uniformizations and selections: Kuratowski, Ryll-Nardzewski selection theorem, Jankov-von Neumann uniformization theorem, Michael selection theorem, projections and uniformizations of sets with large sections (in the sense of measure or category), projections and uniformizations of sets with small sections (countable, compact).

 Entry requirements - ---CzechEnglish
Last update: RNDr. Václav Vlasák, Ph.D. (10.05.2018)

Knowledge at the level of completion of Descriptive Set Theory 1 NMMA433.

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