On a theorem of Arvanitakis

TL;DR

This paper presents a shorter proof of a more general version of Arvanitakis' theorem, which unifies Michael's convex selection theorem and Dugundji's extension theorem, advancing the theoretical understanding of these foundational results.

Contribution

It offers a concise proof of a broader theorem that generalizes two important classical theorems in topology and convex analysis.

Findings

Shorter proof of a more general theorem

Unification of Michael's and Dugundji's theorems

Enhanced theoretical framework

Abstract

Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.