ABSTRACT
A map is a continuous function. A Whitney map for C(X) is a map IJL : C(X) -> [0,1] such that (J,({p}) = 0 for each p e X, /j,(X) = I and, if A, B e C(X) and A is properly contained in B, then [i(A) < ^(B). It is known that for each continuum X, there are Whitney maps for C(X) ([7, Theorem 13.4]). A Whitney level is a set of the form fT1^), where t < I and fji is a Whitney map for C(X}. It is known that the Whitney levels are always subcontinua of C(X) ([7, Theorem 19.9]). Given p e X, A C X and e > 0, the e-ball around p in X is denoted by Bx(£,p) and Nx(e,A) = \J{Bx(e,a) :aeA}.
