This research concentrates on algebraic aspects of dimension theory. The crucial part of the project is to decide whether cell- like images of euclidean 4-space are finite-dimensional. Proving (or disproving) results in cohomological dimension theory which are analogous to results in covering dimension theory is another goal of the project. The answers are known to the analogues of the key question for Euclidean spaces of dimensions other than 4. This is another case where the difficulty of a topological question does not increase with dimension. It is distressing to find that the greatest mysteries concern the space of three dimensions in which we live or the space of four dimensions, which may be viewed as space-time.
