UVk maps and embeddings

Abstract

Let X be the inverse limit of compact n-dimensional polyhedra {Xi,fij} whose bonding maps are UVk-maps. The problem of embedding X into Euclidean (2n−k)-space R2n−k (and more general manifolds) is studied. If the factors,Xi, are manifolds,then there is an embedding theorem. In general, under certain dimensional restrictions, X is CE equivalent to a subcontinuum of R2n−k. In particular, if k = 0 and n ⩾ 3, then some CE image of X embeds in R2n. As a by-product of these results, approximation theorems are obtained.