Reconstructing the topology on monoids and polymorphism clones of the rationals

TL;DR

This paper demonstrates methods to reconstruct topologies on monoids and polymorphism clones of the rational numbers, and extends automatic homeomorphicity results to more complex structures.

Contribution

It introduces techniques for reconstructing topologies on monoids and clones of the rationals and extends automatic homeomorphicity results to generated polymorphism clones.

Findings

Successfully reconstructs topology on endomorphism monoids of rationals.

Shows how to lift automatic homeomorphicity to polymorphism clones.

Provides a framework for analyzing topological structures in algebraic contexts.

Abstract

We show how to reconstruct the topology on the monoid of endomorphisms of the rational numbers under the strict or reflexive order relation, and the polymorphism clone of the rational numbers under the reflexive relation. In addition we show how automatic homeomorphicity results can be lifted to polymorphism clones generated by monoids.