Which self-maps appear as lattice anti-endomorphisms?

TL;DR

This paper establishes a precise criterion for when a self-map on a set can be realized as a lattice anti-endomorphism, linking the map's properties to lattice structures.

Contribution

It provides a necessary and sufficient condition for a self-map to be a lattice anti-endomorphism, clarifying the relationship between maps and lattice structures.

Findings

Characterization of self-maps as lattice anti-endomorphisms

Necessary and sufficient conditions identified

Framework for constructing compatible lattice structures

Abstract

Let f be a self-map of the set A. We give a necessary and sufficient condition for the existence of a lattice structure on A such that f becomes a lattice anti-endomorphism with respect to this structure.