  We investigate some properties of the clopen type semigroup of an action of a
countable group on a compact, $0$-dimensional, Hausdorff space X. We discuss
some characterizations of dynamical comparison (most of which were already
known in the metrizable case) in this setting; and prove that for a Cantor
minimal action $\alpha$ of an amenable group the topological full group of
$\alpha$ admits a dense, locally finite subgroup iff the corresponding clopen
type semigroup is unperforated. We also discuss some properties of clopen type
semigroups of the Stone-\v{C}ech compactifications and universal minimal flows
of countable groups, and derive some consequences on generic properties in the
space of minimal actions of a given countable group on the Cantor space.
