Applications of descriptive set theory in real analysis
| Thesis title in Czech: | |
|---|---|
| Thesis title in English: | Applications of descriptive set theory in real analysis |
| Key words: | Diferencovatelnost reálných funkcí, nekonečné hry, borelovské množiny. |
| English key words: | Differentiability of real functions, infinite games, Borel sets. |
| Academic year of topic announcement: | 2014/2015 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Mathematical Analysis (32-KMA) |
| Supervisor: | doc. RNDr. Miroslav Zelený, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 26.09.2014 |
| Date of assignment: | 26.09.2014 |
| Confirmed by Study dept. on: | 26.01.2015 |
| Guidelines |
| V práci budou zkoumány možné aplikace deskriptivní teorie množin v reálné analýze.
Budou studovány možnosti použití nekonečných her a borelovské klasifikace množin v teorii diferencovatelnosti reálných funkcí se zaměřením na vlastnosti gradientového zobrazení funkce více proměnných. |
| References |
| A. Bruckner, Differentiation of real functions, CRM Monograph Series, 5. American Mathematical Society, Providence, RI, 1994.
Z. Buczolich, Solution to the gradient problem of C. E. Weil, Rev. Mat. Iberoamericana 21 (2005), no. 3, 889–910. A.S.Kechris: Classical descriptive set theory, Springer-Verlag, 1994. Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69, (1950). 1–54. M. Zelený, The Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables, Ann. Inst. Fourier. 58 (2008), 405-428. |