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Recently, the holographic aspects of asymptotically de Sitter spacetimes havegenerated substantial literary interest. The plot continues in this paper, aswe investigate a certain class of dilatonically deformed ``topological'' deSitter solutions (which were introduced in hep-th/0110234). Although suchsolutions possess a detrimental cosmological singularity, their interpretationfrom a holographic perspective remains somewhat unclear. The current focus ison the associated generalized $C$-functions, which are shown to maintain theirusual monotonicity properties in spite of this exotic framework. These findingssuggest that such topological solutions may still play a role in ourunderstanding of quantum gravity with a positive cosmological constant.Comment: Latex, 30 pages; reference added and minor changes to tex

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

de Sitter–holographic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi></mml:math>functions with a topological, dilatonic twist

de Sitter–holographicCfunctions with a topological, dilatonic twist