Exceptional Sets in Mathematical Analysis
| Thesis title in Czech: | Výjimečné množiny v matematické analýze |
|---|---|
| Thesis title in English: | Exceptional Sets in Mathematical Analysis |
| Key words: | sigma-pórovitá množina, elementární submodel, Banachův prostor, c-odstranitelná množina, konvexní funkce |
| English key words: | sigma-porous set, elementary submodel, Banach space, c-removable set, convex function |
| Academic year of topic announcement: | 2010/2011 |
| Thesis type: | dissertation |
| Thesis language: | angličtina |
| Department: | Department of Mathematical Analysis (32-KMA) |
| Supervisor: | prof. RNDr. Ondřej Kalenda, Ph.D., DSc. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 11.10.2010 |
| Date of assignment: | 11.10.2010 |
| Date and time of defence: | 11.09.2014 14:00 |
| Date of electronic submission: | 08.08.2014 |
| Date of submission of printed version: | 11.08.2014 |
| Date of proceeded defence: | 11.09.2014 |
| Opponents: | doc. RNDr. Petr Holický, CSc. |
| doc. RNDr. Ondřej Zindulka, CSc. | |
| Guidelines |
| Student bude zkoumat deskriptivní vlastnosti slabých topologií na Banachových prostorech se zaměřením na K-analytické prostory a související třídy. Součástí studia bude i zkoumání a klasifikace podtříd K-analytických topologických prostorů. |
| References |
| [1] Argyros, S. A.; Arvanitakis, A. D.; Mercourakis, S. K. Talagrand's K_sigmadelta problem. Topology Appl. 155 (2008), no. 15, 1737-1755.
[2] Argyros, S. A.; Arvanitakis, A. D.; Mercourakis, S. K. Reznichenko families of trees and their applications. J. Math. Anal. Appl. 350 (2009), no. 2, 792--810. [3] Fabian, Marián J. Gâteaux differentiability of convex functions and topology. Weak Asplund spaces. Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1997. xiv+180 pp. ISBN: 0-471-16822-X [4] Mercourakis, Sophocles. On weakly countably determined Banach spaces. Trans. Amer. Math. Soc. 300 (1987), no. 1, 307-327. Další zejména časopisecká literatura dle potřeby. |
| Preliminary scope of work |
| Studium slabých topologií na Banachových prostorech, zejména s ohledem na K-analytičnost. |
| Preliminary scope of work in English |
| Study of weak topologies on Banach spaces with focus on K-analyticity. |