We obtain a (5 + 2)-dimensional global flat embedding of the (3 + 1)-dimens
ional curved RN-AdS space. Our results include the various limiting cases o
f global embedding Minkowski space (GEMS) geometries of the RN, Schwarzschi
ld-AdS space-time in 5 + 2 dimensions, Schwarzschild space-time in 5 + 1 di
mensions, purely charged space, and universal covering space of AdS space-t
ime in 4 + 1 dimensions, through the successive truncation procedure of par
ameters in the original curved space.