We describe how conformal Minkowski, dS- and AdS-spaces can be united into a
single submanifold [N] of RP^5. It is the set of generators of the null cone in
M^{2,4}. Conformal transformations on the Mink-, dS- and AdS-spaces are induced
by O(2,4) linear transformations on M^{2,4}. We also describe how Weyl
transformations and conformal transformations can be resulted in on [N]. In
such a picture we give a description of how the conformal Mink-, dS- and
AdS-spaces as well as [N] are mapped from one to another by conformal maps.
This implies that a CFT in one space can be translated into a CFT in another.
As a consequence, the AdS/CFT-correspondence should be extended.