On Baire one point of funtions

• Autorzy: Pawlak R. J. , Świątek B.
• Języki publikacji: EN

Abstrakty

EN

We show that the subspace of the space of almost continuous first recoverable with respect to some trajectory {xn} functions, consisting of first return continuous functions with respect to {xn}, is porous at each point of whole space. Next we define a class of strongly F-almost everywhere first return recoverable functions and we describe some properties of these functions. We also prove that the subspace of the space of strongly F-almost everywhere first return recoverable functions consisting of measurable functions is superporous at each point of whole space.

Słowa kluczowe

EN

functions; Darboux Baire; points

PL

funkcje; punkty

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 1
• Strony: 53--64
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Pawlak R. J.

• Department of Mathematics, Łódź University, Banacha 22, 90-238 Łódź, Poland

autor

Świątek B.

• Institute of Mathematics, Technical University of Lodz, Al. Politechniki 11, 90-924 Lodz, Poland

Bibliografia

• [1] U. B. Darji, M. J. Evans and R. J. O'Malley, A first return characterization of Baire one functions, Real Analysis Exchange 19 (1993-94), 510-515.
• [2] U. B. Darji, M. J. Evans and R. J. O'Malley, First return path systems: differentiability, continuity, and orderings, Act a Math. Hungar . 66 (1-2) (1995), 83-103.
• [3] U. B. Darji, M. J. Evans and R. J. O'Malley, Some interesting small subclasses of the Darboux Baire 1 functions, Real Analysis Exchange 19(1) (1993-94), 328-331.
• [4] M. J. Evans and R. J. O'Malley, Fine tuning the recoverability of Baire one functions, Real Analysis Exchange 21(1) (1995-96), 165-174.