Continuous images of products of separable spaces

The aim of this note is to show, using elementary submodels, the following result: “Let X be a space of countable tightness which is the continuous image of a product of separable spaces. Then X is separable”. As a corollary we obtain that if a space of countable tightness is the continuous closed image of a product of separable metrizable spaces then it is the continuous closed image of a separable metrizable space. For notation and terminology we refer the reader to the work of Engelking (1989) and Hodel (1984). Our approach to elementary submodels follows that of Watson (1994).