  In some scientific fields, a scaling is able to modify the topology of an
observed object. Our goal in the present work is to introduce a new formalism
adapted to the mathematical representation of this kind of phenomenon. To this
end, we introduce a new metric structure - the galactic spaces - which depends
on an ordered field extension of R. Moreover, some natural transformations of
the category of galactic spaces, the contractions, are of particular interest:
they generalize usual homotheties, they have a ratio which may be an
infinitesimal, they are able to modify the topology and they satisfy a nice
composition rule. With the help of nonstandard extensions we can associate to
any metric space an infinite family of galactic spaces; lastly, we study some
limit properties of this family.
