  In 5D relativity, the usual 4D cosmological constant is determined by the
extra dimension. If the extra dimension is spacelike, one can get a positive
cosmological constant $\Lambda$ and a 4D de Sitter (dS) space. In this paper we
present that, if the extra dimension is timelike oppositely, the negative
$\Lambda$ will be emerged and the induced 4D space will be an asymptotic
Anti-de Sitter (AdS). Under the minimum assumption, we solve the Kaluza-Klein
equation $R_{AB} = 0$ in a canonical system and obtain the AdS solution in a
general case. The result shows that an AdS space is induced naturally from a
Kaluza-Klein manifold on a hypersurface (brane). The Lagrangian of test
particle indicates the equation of motion can be geodesics if the 4D metric is
independent of extra dimension. The causality is well respected because it is
appropriately defined by a null higher dimensional interval. In this 5D
relativity, the holographic principle can be used safely because the brane is
asymptotic Euclidean AdS in the bulk. We also explore some possible holographic
duality implications about the field/operator correspondence and the two-points
correlation functions.
