The Bing staircase construction for 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...

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

Diffeomorphisms for Hilbert Manifolds and Handle Decomposition

1. We announce here the following result: Two homotopic diffeomorphisms of a paracompact separable Hubert manifold of infinite dimension are isotopic. (1) In this paper, a hilbert manifold (A-manifold) with or without boundary is always hausdorff, paracompact, separable C°°-differentiable and with the infinite dimensional separable hilbert space H as local model. Let M(M, dM) be an /^-manifold ...