  Since the solution of the so-called folk problems of smoothability, there has
been a special interest in the properties of classical time and volume
functions of spacetimes. Here we supply some information that complements the
one provided in arXiv:1108.5120v3 and arXiv:1301.2909v1, and discuss some
results. As an illustration, we show that any Cauchy temporal function for a
globally hyperbolic spacetime remains Cauchy temporal for close metrics
---which, in particular, implies stability for global hyperbolicity.
