Geometry and Topology

[msu_math]

Geometry is the study of shapes and space, in particular, groups of transformations that act on spaces. For example, projective geometry is about the group of projective transformations that act on the real projective plane, whereas inversive geometry is concerned with the group of inversive transformations acting on the extended complex plane.

Geometry has been extended to topology, which deals with objects known as topological spaces and continuous maps between them. Topology is concerned with the way in which a space is connected and ignores precise measurements of distance or angle.