  We construct a positive constant curvature space by identifying some points
along a Killing vector in a de Sitter Space. This space is the counterpart of
the three-dimensional Schwarzschild-de Sitter solution in higher dimensions.
This space has a cosmological event horizon, and is of the topology ${\cal
M}_{D-1}\times S^1$, where ${\cal M}_{D-1}$ denotes a $(D-1)$-dimensional
conformal Minkowski spacetime.
