About subtransversality of collections of sets

TL;DR

This paper introduces dual conditions for subtransversality of set collections in Banach and Asplund spaces, proposing a new intermediate concept called weak intrinsic subtransversality.

Contribution

It provides dual sufficient conditions in Asplund spaces and a necessary and sufficient criterion for convex sets in Banach spaces, along with a new intermediate transversality notion.

Findings

Dual sufficient conditions for subtransversality in Asplund spaces

Necessary and sufficient dual criterion for convex sets in Banach spaces

Introduction of weak intrinsic subtransversality as an intermediate concept

Abstract

We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.