Real Analysis Exchange

On Some Subclasses of Baire 1 Functions

Ryszard J. Pawlak, Ilona Ćwiek, and Bożena Świątek

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Abstract

We will consider the classes of first return continuous, weakly first return continuous with respect to some trajectory and almost continuous functions in the sense of Stallings and we will show that for the Baire $1$ functions the classes of functions mentioned above are equal. Moreover we will define the class $\mathcal{B}_{1}^{\mathcal{F}}$ of strongly $\mathcal{F}$-almost everywhere first return recoverable functions and shall present the relation between family $\mathcal{B}_{1}^{\mathcal{F}}$ and Baire $1$ functions.

Article information

Source
Real Anal. Exchange, Volume 27, Number 2 (2001), 415-422.

Dates
First available in Project Euclid: 2 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212412845

Mathematical Reviews number (MathSciNet)
MR1922658

Zentralblatt MATH identifier
1048.26006

Subjects
Primary: 26A21: Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50, 54H05] 54C30: Real-valued functions [See also 26-XX] 54C35: Function spaces [See also 46Exx, 58D15]

Keywords
trajectory first return recoverable function first return continuous function Baire 1 function

Citation

Ćwiek, Ilona; Pawlak, Ryszard J.; Świątek, Bożena. On Some Subclasses of Baire 1 Functions. Real Anal. Exchange 27 (2001), no. 2, 415--422. https://projecteuclid.org/euclid.rae/1212412845


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References

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