In the year 2016 Wen Huang, Danylo Khilko, Sergii Kolyada and Guohua Zhang published an article on dynamical compactness and sensitivity where they introduced the concept of ωNT-limit sets and transitive compactness to connect the Auslander point dynamics with topological transitivity. In this paper we study the properties of ωNT-limit sets of chaotic dynamical systems (X,T) given by a compact metric space X and a surjective map T : X -> X and show that if we restrict ourselves to interval mappings, then transitive compactness and weak mixing are equivalent. Lastly, we discuss open problems.