Conservative median algebras and semilattices

TL;DR

This paper characterizes conservative median algebras and semilattices through forbidden substructures and chain representations, and describes median-preserving maps using duality with topological structures.

Contribution

It introduces a characterization of conservative median algebras and semilattices via forbidden substructures and duality theory, providing new insights into their structure and mappings.

Findings

Median algebras are characterized by forbidden substructures.

Conservative median algebras are represented as chains.

Descriptions of median-preserving maps between product chains are provided.

Abstract

We characterize conservative median algebras and semilattices by means of forbidden substructures and by providing their representation as chains. Moreover, using a dual equivalence between median algebras and certain topological structures, we obtain descriptions of the median-preserving mappings between products of finitely many chains.