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A certain class K of GR homogeneous spacetimes is considered. For each pair E,  of spacetimes from K,  where conformal transformation g is from . Each E (being  or its double cover, as a manifold) is interpreted as related to an observer in Segal’s universal cosmos. The definition of separation d between E and  is based on the integration of the conformal factor of the transformation g. The integration is carried out separately over each region where the conformal factor is no less than 1 (or no greater than 1). Certain properties of  are proven; examples are considered; and possible directions of further research are indicated.

On Separation between Metric Observers in Segal’s Compact Cosmos