Mahaney's Theorem states that there are no sparse NP-complete problems
if P not equal NP. We propose an adaptation of that theorem to the Bl
um-Shub-Smale model of computation of the reals with addition and equa
lity. In that setting, sparseness is defined in terms of topological d
imension instead of cardinality. (C) 1997 Elsevier Science B.V.