Characterizations of some transversality-type properties

TL;DR

This paper provides primal and slope characterizations of various transversality properties, clarifies their relations, and establishes the metric nature of intrinsic transversality, extending existing results to Banach spaces.

Contribution

It introduces new primal and slope characterizations of transversality properties and extends the understanding of intrinsic transversality to Banach spaces.

Findings

Metric nature of intrinsic transversality established

Relation between intrinsic and tangential transversality clarified

Equivalence with prior Hilbert space characterizations proved

Abstract

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.