It is well-known that the global structure of every space-time model for relativistic cosmology is observationally underdetermined. In order to alleviate the severity of this underdetermination, it has been proposed that we adopt the Cosmological Principle because the Principle restricts our attention to a distinguished class of space-time models (spatially homogeneous and isotropic models). I argue that, even assuming the Cosmological Principle, the topology of space remains observationally underdetermined. Nonetheless, I argue that we can muster reasons to prefer various topological properties over others. In particular, I favor the adoption of multiply connected universe models on grounds of (i) simplicity, (ii) Machian considerations, and (iii) explanatory power. We are able to appeal to such grounds because multiply connected topologies open up the possibility of finite universe models (consistent with our best data), which in turn avoid thorny issues concerning the postulation of an actually infinite universe.

众所周知，相对论宇宙学的每个时空模型的全局结构在观测上都是不确定的。为了减轻这种不确定性的严重性，有人建议我们采用宇宙学原理，因为该原理将我们的注意力限制在一类特殊的时空模型（空间均匀和各向同性模型）上。我认为，即使假设宇宙学原理，空间的拓扑结构在观测上仍然是不确定的。尽管如此，我认为我们可以找出理由来选择各种拓扑性质而不是其他性质。特别是，我赞成采用多重连接的宇宙模型，理由是（i）简单性，（ii）马赫主义考虑，以及（iii）解释力。我们之所以能够诉诸这样的理由，是因为多重连接的拓扑开启了有限宇宙模型的可能性（与我们最好的数据一致），这反过来又避免了关于实际无限宇宙假设的棘手问题。