Shape-invariant Neighborhoods of Nonsaddle Sets

Asymptotically stable attractors are only a particular case of a large family of invariant compacta whose global topological structure is regular. We devote this paper to investigating the shape properties of this class of compacta, the nonsaddle sets. Stable attractors and unstable attractors having only internal explosions are examples of nonsaddle sets. The main aim of this paper is to generalize the well-known theorem for the shape of attractors to nonsaddle sets using the intrinsic approach to shape which combines continuity up to a covering and the corresponding homotopies of first order.