A refined transversality theorem on linear perturbations and its applications

TL;DR

This paper introduces a refined transversality theorem related to linear perturbations, utilizing Hausdorff measures, and demonstrates its applications in singularity theory and multiobjective optimization.

Contribution

It presents a new perspective on transversality theorems using Hausdorff measures and applies this to both singularity theory and multiobjective optimization.

Findings

Established a refined transversality theorem based on Hausdorff measures.

Applied the theorem to singularity theory.

Extended applications to multiobjective optimization.

Abstract

In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.