On set star-menger spaces

Abstract

In this paper, we prove that the product of a set star-Menger space with a compact space is a rectangular set star-Menger. We also  provide an example of Tychonoff pesudocompact set star-Menger space which is not set strongly starMenger. The above mentioned  results answer two questions of [14]. We show that the product of a SSM space with a compact space is not set-SSM, which gives a partial  answer to another question of [14] negatively.