1-dimensional phenomena in cell-like mappings on 3-manifolds
Robert J. Daverman · Pacific Journal of Mathematics · 1988
Two 1-dimensional phenomena are studied.One resides in the 3manifold domain of a cell-like map /: M 3 -> Y and consists of an infinite 1-skeleton X on which / is 1-1; if, in addition, the nondegeneracy set of/ misses a dense natural embedding in A/ is a 3-manifold except possibly at points of a 1-complex F, topologically embedded in Y as a closed subset, then / can be approximated by another cell-like map p: M -> Y whose no embedding dimension < 1 and / x Id: M 3 x approximated by homeomorphisms.