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### On the insertion of Darboux functions

Fundamenta Mathematicae

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.

### Connectivity of diagonal products of Baire one functions

Fundamenta Mathematicae

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.

### Separating sets by Darboux-like functions

Fundamenta Mathematicae

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).

### Maximums of Darboux Baire one functions

Mathematica Slovaca

### Maximums of Darboux quasi-continuous functions

Mathematica Slovaca

### On the differences of upper semicontinuous quasi-continuous functions

Mathematica Slovaca

### Averages of quasi-continuous functions

Mathematica Bohemica

The goal of this paper is to characterize the family of averages of comparable (Darboux) quasi-continuous functions.

### On theorems of Pu & Pu and Grande

Mathematica Bohemica

Given a finite family of cliquish functions, , we can find a Lebesgue function $\alpha$ such that $f+\alpha$ is Darboux and quasi-continuous for every $f\in$. This theorem is a generalization both of the theorem by H. W. Pu H. H. Pu and of the theorem by Z. Grande.

### On multiplication in spaces of continuous functions

Colloquium Mathematicae

We introduce and examine the notion of dense weak openness. In particular we show that multiplication in C(X) is densely weakly open whenever X is an interval in ℝ.

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