On tangential transversality

TL;DR

This paper introduces the concept of tangential transversality for closed sets in Banach spaces, providing a unified framework that bridges known and new results without relying on variational principles.

Contribution

It defines tangential transversality as an intermediate property and demonstrates its utility in deriving various results through primal space conditions.

Findings

Introduces tangential transversality as a new concept.

Provides unified proofs of existing results.

Derives new results using primal space conditions.

Abstract

This is the first of two closely related papers on transversality. Here we introduce the notion of tangential transversality of two closed subsets of a Banach space. It is an intermediate property between transversality and subtransversality. Using it, we obtain a variety of known results and some new ones in a unified way. Our proofs do not use variational principles and we are concentrated mainly on tangential conditions in the primal space.