A weakly mixing dynamical system with the whole space being a transitive extremal distributionally scrambled set.

It is known that the whole space can be a Li–Yorke scrambled set in a compact dynamical system, but this does not hold for distributional chaos. In this paper we construct a noncompact weekly mixing dynamical system, and prove that the whole space is a transitive extremal distributionally scrambled set in this system. [ABSTRACT FROM AUTHOR]