  We present a model in which a gauge symmetry of a field theory is intrinsic
in the geometry of an extended space time itself. A consequence is that the
dimension of our space time is restricted through the BRS cohomology. If the
Hilbert space is a dense subspace of the space of all square integrable
$C^{\infty}$ functions, the BRS cohomology classes are nontrivial only when the
dimension is two or four.
