Geometrically, topologywas the study of properties preserved by a certain group of transformations, the homeomorphisms. Geometry itself can be considered as thestudy of properties preserved by certain types of functions; e.g., Euclideanmetric geometry is the study of properties preserved by rigid (that is,distance-preserving) transformations (known sometimes as congruences).(Of course, as with topology, it is somewhat unfair to try to define geometry as the study of one particular thing.)