Alternate proofs for the $n$-dimensional resolution theorems

We present new, unified proofs for the cell-like, $\mathbb{Z}\mathrm{/}p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems involving cohomology groups by converting them into problems about homology groups. We provide a coordinated general topological method for constructing the maps needed to witness the resolution theorems simultaneously.