Characterization of hereditarily reversible posets

TL;DR

This paper characterizes hereditarily reversible posets and preordered sets using forbidden subsets, extending known examples of hereditarily reversible topological spaces.

Contribution

It provides a complete characterization of hereditarily reversible posets and preordered sets in terms of forbidden subsets, expanding the understanding of these structures.

Findings

Characterization of hereditarily reversible posets and preordered sets.

Extension of known examples of hereditarily reversible topological spaces.

Identification of forbidden subsets for these classes.

Abstract

A poset P is called reversible if every order preserving bijective self map of P is an order automorphism. P is called hereditarily reversible if every subposet of P is reversible. We give a complete characterization of hereditarily reversible posets in terms of forbidden subsets. A similar result is stated also for preordered sets. As a corollary we extend the list of known examples of hereditarily reversible topological spaces.