Projection as Affine Transformation

Question

$S \subseteq \mathbb{R}^m \times \mathbb{R}^n$ is projected onto some of its coordinates: $$T = \{x_1 \in \mathbb{R}^m | \ (x_1,x_2)\in S \text{ for some } x_2 \in \mathbb{R}^n \}. $$

Can I show this projection as an affine map?

Answer 1

This projection is a linear map of the type $$ F(x_1,x_2) = x_1. $$ Then $T = F(S)$ is convex if $S$ is convex.