  We examine three primal space local Hoelder type regularity properties of
finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and
uniform [q]-regularity as well as their quantitative characterizations.
Equivalent metric characterizations of the three mentioned regularity
properties as well as a sufficient condition of [q]-subregularity in terms of
Frechet normals are established. The relationships between [q]-regularity
properties of collections of sets and the corresponding regularity properties
of set-valued mappings are discussed.
