Selections and Higher Separation Axioms

TL;DR

This survey reviews the history and recent progress in the theory of selections for set-valued mappings, highlighting open questions and potential applications in topology and analysis.

Contribution

It provides a comprehensive overview of the development and current state of selection theory for set-valued mappings, including unresolved problems.

Findings

Historical background of selection theory

Recent advancements in selection theorems

Open questions in the field

Abstract

This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in the selection problem for set-valued mappings --- a problem with a fascinating history and appealing applications.