Aditivní systémy borelovských množin
| Thesis title in Czech: | Aditivní systémy borelovských množin |
|---|---|
| Thesis title in English: | Additive families of Borel sets |
| Academic year of topic announcement: | 2018/2019 |
| Thesis type: | diploma thesis |
| Thesis language: | čeština |
| 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: | 23.05.2018 |
| Date of assignment: | 24.05.2018 |
| Confirmed by Study dept. on: | 13.07.2018 |
| Date and time of defence: | 30.06.2020 09:00 |
| Date of electronic submission: | 05.01.2020 |
| Date of submission of printed version: | 05.01.2020 |
| Date of proceeded defence: | 30.06.2020 |
| Opponents: | prof. RNDr. Jiří Spurný, Ph.D., DSc. |
| Guidelines |
| Předmětem práce je seznámení se s některými pojmy neseparabilní deskriptivní teorie množin podle uvedené literatury s ohledem na otevřený problém, zda každý bodově spočetný borelovsky aditivní systém podmnožin úplného metrického prostoru má sigma-diskrétní zjemnění. |
| References |
| Fleissner, W. G., An axiom for nonseparable Borel theory, Trans. Amer. Math. Soc. 251 (1979), 309-328.
D. H. Fremlin, Measure-additive coverings and measurable selectors. Dissertationes Math. 260(1987). Hansell, R. W., Borel measurable mappings for nonseparable metric spaces, Trans. Amer. Math. Soc. 161 (1971), 145-169. Hansell, R. W., F-sigma set covers of analytic spaces and first class selectors, Proc. Amer. Math. Soc. 96 (1986), 365-371. Kaniewski, J., Pol, R., Borel-measurable selectors for compact-valued mappings in the non-separable case, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 23 (1975), 1043-1050. Spurný, J., G-delta additive families in absolute Souslin spaces and Borel measurable selectors, Topology Appl. 154 (2007), 2779-2785. Spurný, J., Zelený, M., Additive families of low Borel classes and Borel measurable selectors, to appear in Canad. Math. Bull. (2011). |
| Preliminary scope of work |
| Podrobnosti jsou k dispozici na adrese http://www.karlin.mff.cuni.cz/~zeleny/mff/Diplomka_Aditivni_systemy_borelovskych_mnozin.pdf |
| Preliminary scope of work in English |
| Details can be found at http://www.karlin.mff.cuni.cz/~zeleny/mff/Diplomka_Aditivni_systemy_borelovskych_mnozin.pdf |