  This paper is about lower and upper bounds for the Hausdorff dimension of the
level and collision sets of a class of Feller processes. Our approach is
motivated by analogous results for L\'evy processes by Hawkes (for level sets),
Taylor and Jain & Pruitt (for collision sets). Since Feller processes lack
independent or stationary increments, the methods developed for L\'evy
processes cannot be used in a straightforward manner. Under the assumption that
the Feller process possesses a transition probability density, which admits
lower and upper bounds of a certain type, we derive sufficient conditions for
regularity and non-polarity of points; together with suitable time changes this
allows us to get upper and lower bounds for the Hausdorff dimension.
