LOTS as Fixed Point Sets: An Application of Tarski's Fixed Point Theorem (draft)

TL;DR

This paper explores the properties of linearly ordered topological spaces (LOTS), such as real numbers and ordinals, using Tarski's Fixed Point Theorem to analyze their fixed point sets.

Contribution

It applies Tarski's Fixed Point Theorem to LOTS, providing new insights into their fixed point sets and topological properties.

Findings

LOTS include important spaces like reals, rationals, and ordinals

Fixed point sets in LOTS have rich topological structures

The study reveals non-hereditary properties of LOTS topologies

Abstract

This article has been withdrawn in 2013. The class of LOTS (linearly ordered topological spaces) contains many important spaces, like the set of real numbers, the set of rational numbers and the ordinals. Such spaces have rich topological properties, which are not necessarily hereditary.