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 Sep 2024


Gemignani, Michael C. Elementary Topology. 2nd ed. AddisonWesley Series in Mathematics. Reading, MA: AddisonWesley Publishing Company, 1971.

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,distancepreserving) 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.)
