The importance of studying spatial cognition in cognitive science is enforced by the fact that the applicability of spatial concepts and spatial expressions is not limited to the spatial domain. We claim that common structures underlying both concrete, physical space and other domains are the basis for using spatial expressions, e.g., prepositions like between, with respect to space as well as time or other domains. This claim opposes the thesis that the common use is based upon an analogy between concrete space and other domains. The development of geometry from Euclid's Elements to more differentiated systems of diverse geometries and topologies can be perceived of as an example of the transfer from modeling concrete space towards describing abstract spatial structures.