Stability, open embeddings, and classification of bounded weak- ∗ manifolds

Abstract

It is known that the following spaces are homeomorphic: (1) a separable, reflexive, infinite-dimensional Banach space with its bounded weak topology, (2) the conjugate of a separable, infinite-dimensional Banach space with its bounded weak- ∗ topology, and (3) Q ∞ = dir lim Q n , where Q is the illbert cube. Let F denote one of the above three spaces, and let M and N denote paraimpact, connected F manifolds. Here we prove that M × F is homeomorphic to M. Combined with previous work of the author this result implies that M, embeds as an open subset of F and that if M and N have the same homotopy type then they are homeomorphic.