  Motivated by a number of research questions concerning transversality-type
properties of pairs of sets recently raised by Ioffe and Kruger, this paper
reports several new characterizations of the intrinsic transversality property
in Hilbert spaces. Our dual space results clarify the picture of intrinsic
transversality, its variants and the only existing sufficient dual condition
for subtransversality, and actually unify them. New primal space
characterizations of the intrinsic transversality which is originally a dual
space condition lead to new understanding of the property in terms of primal
space elements for the first time. As a consequence, the obtained analysis
allows us to address a number of research questions asked by the two
aforementioned researchers about the intrinsic transversality property in the
Hilbert space setting.
