  In this paper we attempt to present a very general approach to the study of
structures (somehow) defined on a set $X$ by a family of maps $d: X \times X
\mapsto \mathbb{R}^+$. It will be shown how the assignment of a preorder
$\prec_{\Pi}$ on a set $\Pi$ of families of maps from $X \times X$ into
$\mathbb{R}^+$ defines a structure on $X$. The structures obtained in this way
will be called \emph{real structures}. For real structures on two different
sets we study when they are \emph{of the same type}. An answer to this question
will allow to introduce the notion of \emph{morphism}, and then to give the
definition of the initial real structure with respect to a family of maps, and
so also the definition of product real structure. Various examples of
preorders, and hence of real structures, will be exhibited and discussed. A few
examples of morphisms will be proposed.
