Theory of real functions and descriptive set theory II
Project goals
The project is based on the long-termed research of the applicants. We will continue our research in the differentiability theory of real functions, where we will concentrate on open problems concerning smallness of sets of non-differentiability points(in Fréchet and Gateaux sense) of Lipschitz, convex and semiconvex functions in Banach spaces. We will be solving a number of other problems about general semiconvex functions. We will try to solve some problems concerning Dini derivatives of real functions of one variable. We will continue the study of d.c. (delta-convex) functions and mappings, and its generalizations. We will also investigate real-analytic properties of weakly differentiable mappings (Sobolev and BV mappings). We will study properties of Borel sets and mappings, especially the possibility of improvement of well-known theorems about Borel uniformizations. We will work in the abstract theory of systems of compact sets in Polish metric spaces, and also investigate properties of concrete systems coming, for example, from harmonic analysis.
Keywords
reálné funkcediferencovatelnostborelovská množinasigma-ideálkonvexita
Public support
Provider
Czech Science Foundation
Programme
Standard projects
Call for proposals
Standardní projekty 12 (SGA02009GA-ST)
Main participants
—
Contest type
VS - Public tender
Contract ID
201/09/0067
Alternative language
Project name in Czech
Teorie reálných funkcí a deskriptivní teorie množin II
Annotation in Czech
Cílem jsou nové výsledky v těchto oblastech: Diferencovatelnost lipschitzovských, konvexních a semikonvexních funkcí; reálně-analytické vlastnosti slabě diferencovatelných zobrazení; vlastnosti borelovských množin a zobrazení v úplných prostorech; deskriptivní vlastnosti systémů kompaktních množin.
Scientific branches
Completed project evaluation
Provider evaluation
V - Vynikající výsledky projektu (s mezinárodním významem atd.)
Project results evaluation
The project was excellent, both in terms of expertise and in terms of disbursement of funds.
Solution timeline
Realization period - beginning
Jan 1, 2009
Realization period - end
Dec 31, 2011
Project status
U - Finished project
Latest support payment
Apr 16, 2011
Data delivery to CEP
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data delivery code
CEP12-GA0-GA-U/02:2
Data delivery date
May 2, 2016
Finance
Total approved costs
840 thou. CZK
Public financial support
840 thou. CZK
Other public sources
0 thou. CZK
Non public and foreign sources
0 thou. CZK
Basic information
Recognised costs
840 CZK thou.
Public support
840 CZK thou.
100%
Provider
Czech Science Foundation
CEP
BA - General mathematics
Solution period
01. 01. 2009 - 31. 12. 2011