The Bing staircase construction for Hilbert cube manifolds

Abstract

Finite dimensional techniques of Bing and Bryant are extended to Hilbert cube manifolds to show that $\text{M}\text{A}\text{× Q = M}$ where M is a Hilbert cube manifold, A is an embedded copy of 1^k, 0$\text{}\text{̌}$k$\text{}\text{̌}$∞, and Q is the Hilbert cube. Among the corollaries given here are elementary proofs of two theorems of West: the mapping cylinder theorem and the sum theorem for Hilbert cube factors.