ON UNIQUE RECOVERABILITY OF CONVEX AND VISIBLE COMPACTA FROM THEIR PROJECTIONS

Abstract

The question is: Under what conditions does the congruence of the projections of two compacta on every two-dimensional plane imply the congruence of the compacta themselves? The results are extended to the cases of (n – 2)-visible and (n – 2)-convex compacta, and even to the case when it is known the projections of the compacta are merely similar.