  In this paper, we introduce a family of topological spaces that captures the
existence of preservation theorems. The structure of those spaces allows us to
study the relativisation of preservation theorems under suitable definitions of
surjective morphisms, subclasses, sums, products, topological closures, and
projective limits. Throughout the paper, we also integrate already known
results into this new framework and show how it captures th essence of their
proofs.
