When is $X\times Y$ homeomorphic to $X\times_l Y$?

TL;DR

This paper investigates conditions under which the product of certain linearly ordered topological spaces is homeomorphic or embeddable into spaces with similar properties, advancing understanding of ordered topological product structures.

Contribution

It identifies a class of linearly ordered spaces where the product with itself is homeomorphic or embeddable into a linearly ordered space with the same property.

Findings

Identifies conditions for $X\times X$ to be homeomorphic to $X\times_l X$

Provides partial results supporting the conjectures

Explores embeddings into linearly ordered spaces

Abstract

We identify a class of linearly ordered topological spaces $X$ that may satisfy the property that $X\times X$ is homeomorphic to $X\times_l X$ or can be embedded into a linearly ordered space with the stated property. We justify the conjectures by partial results.