In this paper I have discussed observational relations of cosmological
point sources in some specific waveband, and their use in the context of
data provided by the galaxy redshift surveys. The equations for colour,
K-correction and number counts were presented and discussed in the
context of curved spacetimes, and related to the underlying geometry
of cosmological models. All expressions obtained here are valid for
any cosmological metric, since no specific geometry was assumed in such
a derivation. Although these observables can be specialized for a given
spacetime geometric, some quantities must come from astrophysical
considerations, namely the intrinsic luminosity *L*(*z*), the source
spectrum function
*J*(), and the luminosity
function (*w*).
These cannot be obtained only from geometrical considerations, which means
that the determination of the spacetime structure of universe is a task
intrinsically linked to astrophysical considerations and results.

The application of the general results of this paper to specific cosmological metrics is the subject of a forthcoming paper (Ribeiro 1999).

**Acknowledgements**

I thank FUJB-UFRJ for partial financial support.