  We investigate the role of the proximality relation for tiling dynamical
systems. Under two hypotheses, namely that the minimal rank is finite and the
set of fiber distal points has full measure we show that the following
conditions are equivalent: (i) proximality is topologically closed, (ii) the
minimal rank is one, (iii) the continuous eigenfunctions of the translation
action span the L^2-functions over the tiling space. We apply our findings to
model sets and to Meyer substitution tilings. It turns out that the Meyer
property is crucial for our analysis as it allows us to replace proximality by
the a priori stronger notion of strong proximality.
