We show that for compacta
X,Y ⊂ Rn, n ≧ 5, satisfying the small loops condition and having dimensions in the
trivial range with respect to n, Sh(X) = Sh(Y ) if and only if Rn−X ≈ Rn−Y . As
a corollary we obtain the following result whose statement is void of shape: If
X,Y ⊂ Rn, n ≧ 5, are homeomorphic compacta satisfying the small loops
condition and having dimensions in the trivial range with respect to n, then
Rn− X ≈ Rn− Y .