On Algebraic Properties of the Family of Weakly Świa̧tkowski Functions.

In the paper we will focus on weakly Światkowski functions. We say that f satisfies the weak Świa̧tkowski condition (or f is a weakly Świa̧tkowski function) if for all x 1 , x 2 with f (x 1) < f (x 2) there is a point x between x 1 and x 2 such that f (x 1) < f (x) < f (x 2) . This definition is a modification of the Świa̧tkowski condition, in which point x mentioned above has to be a point of continuity of f. In the paper we will examine some properties of weakly Świa̧tkowski functions and consider lineability and algebrability of some families of functions related to them. [ABSTRACT FROM AUTHOR]