Trivial fibrations of the multiplication maps for monads generated by the functors of order-preserving and positively homogeneous functionals

TL;DR

This paper explores the geometric properties of monads related to order-preserving and positively homogeneous functionals, establishing conditions under which certain multiplication maps form trivial fibrations based on the topological nature of the underlying compact spaces.

Contribution

It characterizes when the multiplication maps of these monads are trivial fibrations, linking this to the openly generated and hi-homogeneous properties of compact spaces.

Findings

The map  X is a trivial I^ au-fibration if and only if X is openly generated hi-homogeneous.

Provides a topological criterion for trivial fibrations of monad multiplication maps.

Extends understanding of the geometric structure of monads in functional analysis.

Abstract

In this paper we further investigate the geometry of monads of order-preserving functionals and of positively homogeneous functionals. We prove that for any compactum X with $w(X) = \tau$ the map $\mu_F X$, where $F\in\{O,OH\}$, is homeomorphic to trivial $I^\tau$-fibration if and only if $X$ is openly generated $\chi$-homogeneous compactum.