The compacta X in $S^n$ for which Sh(X) = Sh($S^k$) is equivalent to $S^n$-X ≈ $S^n$-$S^k$
Volume 97 / 1977
Fundamenta Mathematicae 97 (1977), 79-94
DOI: 10.4064/fm-97-2-79-94