Manifold approximation of set-valued functions

TL;DR

This paper introduces a new form of continuity for set-valued functions and proves an existence theorem for functions satisfying this continuity, advancing the theoretical understanding of set-valued analysis.

Contribution

It presents a novel continuity concept for set-valued functions and establishes an existence theorem, contributing new theoretical tools to the field.

Findings

Introduces a new continuity concept for set-valued functions.

Proves an existence theorem for these continuous set-valued functions.

Enhances theoretical framework of set-valued analysis.

Abstract

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.