  Recently, the holographic aspects of asymptotically de Sitter spacetimes have
generated substantial literary interest. The plot continues in this paper, as
we investigate a certain class of dilatonically deformed ``topological'' de
Sitter solutions (which were introduced in hep-th/0110234). Although such
solutions possess a detrimental cosmological singularity, their interpretation
from a holographic perspective remains somewhat unclear. The current focus is
on the associated generalized $C$-functions, which are shown to maintain their
usual monotonicity properties in spite of this exotic framework. These findings
suggest that such topological solutions may still play a role in our
understanding of quantum gravity with a positive cosmological constant.
