  In this paper we focus our efforts on studying how a preorder and topology
can be made compatible. Thus we provide a characterization of those that are
continuous-compatible. Such a characterization states that such topologies must
be finer than the so-called upper topology induced by the preorder and, thus,
it clarifies which topology is the smallest one among those that make the
preorder continuous. Moreover, we provide sufficient conditions that allows us
to discard in an easy way the continuity of a preference. In the light of the
obtained results, we provide possibility counterparts of the a few celebrate
impossibility theorems for continuous social social intergenerational
preferences due to P. Diamond, L.G. Svensson and T. Sakai. Furthermore, we
suggest quasi-pseudo-metrics as appropriate quantitative tool for reconciling
topology and social intergenerational preferences. Thus, we develop a metric
type method which is able to guarantee possibility counterparts of the
aforesaid impossibility theorems and, in addition, it is able to give numerical
quantifications of the improvement of welfare. We also show that our method
makes always the intergenerational preferences semi-continuous multi-utility
representables in the sense of \"{O}zg\"{u} Evern and Efe O. Ok. Finally, in
order to keep close to the classical way of measuring in the literature, a
refinement of the previous method is presented in such a way that metrics are
involved.
