The Universal Covering Conjecture for closed irreducible orientable 3-manifolds

Let $X$ be a closed, connected, irreducible, orientable 3-manifold with infinite fundamental group. Its universal covering space is denoted by $\widetilde{X}$. Universal Covering Conjecture. The universal covering space

$$\widetilde{X}$$

is homeomorphic to $\mathbf{R}^3$. This is presented as a well-known problem related to the paper's results; its resolution is not specified in the source.