  We calculate corrections to the Bekenstein-Hawking entropy formula for the
five-dimensional topological AdS (TAdS)-black holes and topological de Sitter
(TdS) spaces due to thermal fluctuations. We can derive all thermal properties
of the TdS spaces from those of the TAdS black holes by replacing $k$ by $-k$.
Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and
TdS cases including the cosmological horizon of the Schwarzschild-de Sitter
(SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and
their dynamic correspondences.
