Starting somewhere in the 19th century, mathematics turned from the study of concrete objects to the study of objects satisfying enough properties to lead to interesting theorems. For example:
From permutation groups and groups of geometrical transfomations we got the group axioms.
From ad hoc methods of approximating functions in analysis we got metric spaces.
From metric spaces we got topological spaces.
Are there documented examples of mathematicians from this period explicitly noticing and commenting on this trend (either in mathematics in general, or in a particular field)? In particular, are there examples of resistance to the idea?