Characterizations of some transversality-type properties

Primal characterizations (necessary and sufficient conditions) and slope characterizations of subtransversality, intrinsic transversality and transversality are obtained. The metric nature of intrinsic transversality is established. The relation of intrinsic transversality and tangential transversality is clarified. The equivalence of our characterization of intrinsic transversality and the primal characterization of intrinsic transversality of Thao et al. in the setting of Hilbert spaces is proved, while in general Banach spaces our characterization is less restrictive.