Embeddings of shape classes of compacta in the trivial range
Embeddings of shape classes of compacta in the trivial range
We show that for compacta $X, Y\subset R^{n},~n\geqq 5$, satisfying the small loops condition and having dimensions in the trivial range with respect to $n$, $Sh(X)=Sh(Y)$ if and only if $ R^{n}-X\approx R^{n}- Y$. As a corollary we obtain the following result whose statement is void of shape: If $X, …