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3 Fundamenta Mathematicae

3 Maliszewski A.

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On the insertion of Darboux functions

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Maliszewski A.

Fundamenta Mathematicae

1998

tom 156

nr 3

197-209

The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.

Separating sets by Darboux-like functions

100%

Maliszewski A.

Fundamenta Mathematicae

2002

tom 175

nr 3

271-283

We consider the following problem: Characterize the pairs ⟨A,B⟩ of subsets of ℝ which can be separated by a function from a given class, i.e., for which there exists a function f from that class such that f = 0 on A and f = 1 on B (the classical separation property) or f < 0 on A and f > 0 on B (a new separation property).

Connectivity of diagonal products of Baire one functions

100%

Maliszewski A.

tom 146

nr 1

21-29

We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.