[ewjordan]

> If the curvature were slightly less than 1, the topology would be "closed", meaning it would be finite, and traveling in a straight line ends back where you started.

Doesn't this require the assumption that the spacetime is embedded in a higher dimensional spacetime?

It's been a while, but IIRC there are perfectly valid topologically open cosmologies that have locally sphere-like curvatures (in other words, there's no necessary connection between curvature and topology without adding an embeddability constraint), right?