Proximate fixed property and operations

TL;DR

This paper investigates the proximate fixed point property in topological spaces, examining how it is preserved under various operations like products, cones, suspensions, and joins, especially for span 0 continua.

Contribution

It establishes the proximate fixed point property for complex constructions such as products, cones, suspensions, and joins of span 0 continua, extending previous understanding.

Findings

Proximate fixed point property holds for products of span 0 continua.

The property is preserved under cones and suspensions.

Join operations also maintain the proximate fixed point property.

Abstract

Klee introduced the proximate fixed point property for compacta which is stronger than fixed point property. We consider relations between proximate fixed point property of spaces being result of application of different operations to continua. As an application we show this property for products, cones, suspensions and joins of span 0 continua.