On some rings of Swiątkowski functions (Q1072665)

The author says that a function \(f: R\to R\) is a Swiątkowski function if for each points x,y\(\in R\) such that \(f(x)=f(y)\) there exists a point z of continuity of f such that \(z\in (x,y)\) and f(z)\(\in (f(x),f(y))\). It is known that the sum of two Swiątkowski functions need not be a Swiątkowski function. The paper states (without proofs) some sufficient conditions for the existence of a ring of Swiątkowski functions containing all continuous functions and a fixed Swiątkowski function. These conditions are formulated in terms of Darboux property and the structure of set of points of discontinuity.