  Let $\mathcal{P}$ be a topological property. A.V. Arhangel'skii calls $X$
projectively $\mathcal{P}$ if every second countable continuous image of $X$ is
$\mathcal{P}$. Lj.D.R. Ko$\check{c}$inac characterized the classical covering
properties of Menger, Rothberger, Hurewicz and Gerlits-Nagy in term of
continuous images in $\mathbb{R}^{\omega}$. In this paper we study the
functional characterizations of all projective versions of the selection
properties in the Scheepers Diagram.
