Mapping and fixed point property theorems for inverse limits with set-valued bonding functions

TL;DR

This paper introduces new mapping and fixed point theorems for inverse limits with set-valued bonding functions, enhancing understanding of their topological properties and revisiting foundational results in the field.

Contribution

It provides novel theorems for inverse limits with set-valued bonding functions and revisits key earlier results, advancing the theoretical framework.

Findings

New mapping theorems for inverse limits

Fixed point property theorems established

Revised understanding of inverse limit mappings

Abstract

Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the results from two papers, Mioduszewski's ''Mappings of inverse limits'' and Feuerbacher's ''Mappings of inverse limits revisited''.