Homological selections and fixed-point theorems

TL;DR

This paper develops homological selection theorems for C-spaces and finite-dimensional spaces, and applies them to derive fixed-point theorems for certain set-valued maps, advancing fixed-point theory.

Contribution

It introduces new homological selection theorems for C-spaces and finite-dimensional spaces, and uses these to establish fixed-point results for homologically UV^n set-valued maps.

Findings

Established a homological selection theorem for C-spaces.

Proved a finite-dimensional homological selection theorem.

Derived fixed-point theorems for homologically UV^n set-valued maps.

Abstract

A homological selection theorem for C-spaces, as well as, a finite-dimensional homological selection theorem is established. We apply the finite-dimensional homological selection theorem to obtain fixed-point theorems for usco homologically UV^n set-valued maps.