  Motivated by recent proposals for a de Sitter version of the AdS/CFT
correspondence, we give some topological restrictions on spacetimes of de
Sitter type, i.e., spacetimes with $\Lambda>0$, which admit a regular past
and/or future conformal boundary. For example we show that if $M^{n+1}$, $n \ge
2$, is a globally hyperbolic spacetime obeying suitable energy conditions,
which is of de Sitter type, with a conformal boundary to both the past and
future, then if one of these boundaries is compact, it must have finite
fundamental group and its conformal class must contain a metric of positive
scalar curvature. Our results are closely related to theorems of Witten and Yau
hep-th/9910245 pertaining to the Euclidean formulation of the AdS/CFT
correspondence.
