Contractible Hilbert cube manifolds

Approximate Fibrations and Bundle Maps on Hilbert Cube Manifolds

This paper is concerned with parameterized families of approximate fibrations from a compact Hilbert cube manifold M to a compact polyhedron B. The main result shows how to straighten out certain of these families to be nearly like a product. As an application of this technique, it is shown that an approximate fibration p:M +B can be approximated arbitrarily closely by bundle maps if and only i...

Factoring the Hilbert Cube

In 1964, R. D. Anderson announced [ l ] that the product of a countably infinite collection of dendra is a Hilbert cube (a dendron being a nondegenerate, uniquely arcwise connected, Peano continuum). He and R. H. Bing conjectured in [4] that a countably infinite product of compact contractible complexes is a Hilbert cube. The purpose of this note is to announce the following theorems which affi...

Cartesian Products of Contractible Open Manifolds

Fake Boundary Sets in the Hilbert Cube

For each positive integer n, a o-Z-set B„ in the Hilbert cube 7°° is constructed whose complement s„ = Ix — B„ is not homeomorphic to the pseudointerior j of the Hilbert cube though sn and B„ satisfy: (i) every compact subset of s„ is a Z-set in s„; (ii) s„ X s„ is homeomorphic to s; (iii) Bn admits small maps 7°° -» B„; (iv) s„ satisfies the discrete «-cells property; and (v) Bn is locally (n ...

2 ' Is Homeomorphic to the Hilbert Cube