Some properties of S(n)-θ-closed spaces

Recently Dikranjan and Giuli characterized S(n)-θ-closed spaces in terms of special covers and filters. They also gave some interesting results and examples, as well as listing several open problems. In this paper we give a partial solution to one of the questions they raised. We give conditions that make an S(n)-θ-closed space Katetov S(n). Furthermore, we provide examples which answer three of their questions in the general case.