The dichotomy between traces on d-sets Γ in ℝ n and the density of D(ℝ n \Γ) in function spaces.

A space A (ℝ n ) with A = B or A = F and s ∈ ℝ, 0 < p,q < ∞ either has a trace in L p (Γ), where Γ is a compact d-set in ℝ n with 0 < d < n, or D(ℝ n Γ) is dense in it. Related dichotomy numbers are introduced and calculated. [ABSTRACT FROM AUTHOR]