  First, we review local concepts defined previously. A (local) reference frame
$\mathrm{F}$ can be defined as an equivalence class of admissible spacetime
charts (coordinate systems) having a common domain $\mathrm{U}$ and exchanging
by a spatial coordinate change. The associated (local) physical space is made
of the world lines having constant space coordinates in any chart of the class.
Second, we introduce new, global concepts. The data of a non-vanishing global
vector field $\,v\,$ defines a global "reference fluid". The associated global
physical space is made of the maximal integral curves of that vector field.
Assume that, in any of the charts which make some reference frame $\mathrm{F}$:
(i) any of those integral curves $l$ has constant space coordinates $x^j$, and
(ii) the mapping $l\mapsto (x^j)$ is one-to-one. In that case, the local space
can be identified with a part (an open subset) of the global space.
