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Description
  • 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.  (en)
  • 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.
Title
  • Theory of real functions and descriptive set theory II (en)
  • Teorie reálných funkcí a deskriptivní teorie množin II
skos:notation
  • GA201/09/0067
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  • reálné funkce; diferencovatelnost; borelovská množina; sigma-ideál; konvexita (en)
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  • Řešení projektu proběhlo výtečně, jak z hlediska odborného tak i z hlediska čerpání finančních prostředků. (cs)
  • The project was excellent, both in terms of expertise and in terms of disbursement of funds. (en)
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  • borelovská množina
  • diferencovatelnost
  • sigma-ideál
  • reálné funkce
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