An Example of a Right Loop Admitting Only Discrete Topolization

TL;DR

This paper presents a specific example of a right loop that can only be endowed with the discrete topology, highlighting unique topological properties of such algebraic structures.

Contribution

It provides the first known example of a right loop that admits exclusively the discrete topology, expanding understanding of topological constraints in algebraic loops.

Findings

The right loop admits only the discrete topology.

The example illustrates limitations on topologizing certain algebraic structures.

Supports the study of topological properties in algebraic loops.

Abstract

Being motivated by \cite{sk} and \cite{nms}, an example of a right loop admitting only discrete topolization is given.