Note 168 — APPENDIX IV SPACE, GRAVITATION AND SPACE-TIME

To confine ourselves to a three-dimensional space, if this space were spherical, stars situated at a finite distance would yet have vanishing parallaxes, so that they would appear to be at infinity. For this reason a spherical space, though finite, would manifest itself to us visually as infinite. Theoretically, also, images of stars should form at the antipodes. In an elliptical space, however, these images would coincide with the star itself.

Conversely, a Lobatchewskian space, though of infinite extent, would appear to be finite, since stars at infinity would have a non-vanishing parallax, and so would appear to be situated at a finite distance.