Trees and Homogeneous LOTS

TL;DR

This paper characterizes homogeneous complete linearly ordered topological spaces (CHLOTS), constructs towers of such spaces using ordinal and tree methods, and provides an inductive procedure to describe all CHLOTS.

Contribution

It offers a comprehensive classification and construction method for all homogeneous complete linearly ordered topological spaces (CHLOTS).

Findings

Constructed towers of CHLOTS using ordinal indices.

Extended towers via tree constructions.

Provided an inductive procedure to describe all CHLOTS.

Abstract

We describe those complete linearly ordered topological spaces $X$ which are homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open interval in $X$. Using countable tail-like ordinals as indices, we build towers of distinct CHLOTS. Using tree constructions we are able to extend the towers and to describe an inductive procedure which yields every CHLOTS.