  Starting from a short review of the "classical" space problem in the sense of
the 19th century (Helmholtz -- Lie -- Klein) it is discussed how the challenges
posed by special and general relativity to the classical analysis were taken up
by Hermann Weyl and Elie Cartan. Both mathematicians reconsidered the space
problem from the point of view of transformations operating in the
infinitesimal neighbourhoods of a manifold (spacetime). In a short outlook we
survey further developments in mathematics and physics of the second half of
the 20th century, in which core ideas of Weyl's and/or Cartan's analysis of the
space problem were further investigated (mathematics) or incorporated into
basic theories (physics).
