Abstract. We find large algebraic structures inside the following sets of pathological functions: (i) perfectly everywhere surjective functions, (ii) differentiable functions with almost nowhere continuous derivatives, (iii) differentiable nowhere monotone functions, and (iv) Sierpiński-Zygmund functions. The conclusions obtained on (i) and (iii) are improvements of some already known results.

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It is given a complete characterization of the strict singularity and the disjoint strict singularity of the inclusions E → L 1 + L ∞ for the class of rearrangement invariant function spaces E on the [0, ∞) interval. Their relationship is also analyzed. Suitable criteria are given involving the scale of order continuous weak L p -spaces for 1 < p < ∞.

Abstract.It is studied when inclusions between rearrangement invariant function spaces on the interval [0, ∞) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions