Survey on the Generalized R. L. Moore Problem

We give an updated extended survey of results related to the celebrated unsolved generalized R. L. Moore problem. In particular, we address the problem of characterizing codimension one manifold factors, i.e. spaces $X$ having the property that $X\times \mathbb{R}$ is a topological manifold. A main part of the paper is devoted to many efficient general position techniques, which have been used to solve special cases of this problem.