# When are Borel functions Baire functions?

Fundamenta Mathematicae (1993)

- Volume: 143, Issue: 2, page 137-152
- ISSN: 0016-2736

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topFosgerau, M.. "When are Borel functions Baire functions?." Fundamenta Mathematicae 143.2 (1993): 137-152. <http://eudml.org/doc/211997>.

@article{Fosgerau1993,

abstract = {The following two theorems give the flavour of what will be proved. Theorem. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0,1] to Y coincide if and only if Y is connected and locally connected.Theorem. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class functions from [0,1] to Y coincide if and only if for all finite sequences $U_1,...,U_q$ of nonempty open subsets of Y there exists a continuous function ϕ:[0,1] → Y such that $ ϕ^\{-1\}(U_i) ≠Ø$ for all i ≤ q.
},

author = {Fosgerau, M.},

journal = {Fundamenta Mathematicae},

keywords = {Baire functions; Borel functions; functions of the first class},

language = {eng},

number = {2},

pages = {137-152},

title = {When are Borel functions Baire functions?},

url = {http://eudml.org/doc/211997},

volume = {143},

year = {1993},

}

TY - JOUR

AU - Fosgerau, M.

TI - When are Borel functions Baire functions?

JO - Fundamenta Mathematicae

PY - 1993

VL - 143

IS - 2

SP - 137

EP - 152

AB - The following two theorems give the flavour of what will be proved. Theorem. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0,1] to Y coincide if and only if Y is connected and locally connected.Theorem. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class functions from [0,1] to Y coincide if and only if for all finite sequences $U_1,...,U_q$ of nonempty open subsets of Y there exists a continuous function ϕ:[0,1] → Y such that $ ϕ^{-1}(U_i) ≠Ø$ for all i ≤ q.

LA - eng

KW - Baire functions; Borel functions; functions of the first class

UR - http://eudml.org/doc/211997

ER -

## References

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- [12] M. Laczkowich, Baire 1 functions, Real Anal. Exchange 9 (1983-84), 15-28.
- [13] C. A. Rogers, Functions of the first Baire class, J. London Math. Soc. (2) 37 (1988), 535-544. Zbl0687.54014
- [14] S. Rolewicz, On inversion of non-linear transformations, Studia Math. 17 (1958), 79-83. Zbl0086.10104

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