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New proofs of the above facts are based on specific homogeneity properties of the pseudo-arc and of solenoids of pseudo-arcs. The reader is referred to [5] for hyperspace theory. It is known that if X is the pseudo-arc or a solenoid of pseudo-arcs (see [7] for the definition), then the hyperspace C(X) of all nonvoid subcontinua of X is 2-dimensional. It is proved in [6] that if X is the pseudo-arc, then C(X) is also a Cantor manifold, i.e., no O-dimensional subset separates C(X). In [2] a general theorem is presented that C(X) has this property for an arbitrary metric, nondegenerate continuum X. Our proof of the theorem in the title is an application of the following result [3]. Lemma 1. If X is an n-dimensional, locally compact, connected, homogeneous, metric space, then no (n 2)-dimensional subset separates X(n > 1). Lemma 2. If a dense, connected subset of a metric separable space X is separated by no n-dimensional subset, then the space X has the same property. O (1) Let X be the pseudo-arc. To show that C(X) is a Cantor manifold it suffices to observe, by Lemmas 1 and 2, that the subspace Y c C(X) of all nondegenerate, proper subcontinua of X is connected, locally compact, homogeneous (see [1]), as well as 2-dimensional and dense. (2) Let X be a solenoid of pseudo-arcs with the continuous decomposition D into pseudo-arcs such that X/D is a solenoid S. The set D as a subspace of C(X) is homeomorphic to S. As in (1) the open subspace Y of C(X) is connected and dense. The set Y\D is dense in Y and is the union of two disjoint, open, connected, 2-dimensional subsets M — {yGY:d^ycdGD} Received by the editors February 25, 1989 and, in revised form, November 19, 1989. 1980 Mathematics Subject Classification (1985 Revision). Primary 54B20; Secondary 54F45.

The hyperspaces of subcontinua of the pseudo-arc and of solenoids of pseudo-arcs are Cantor manifolds