A quotient-like construction involving elementary submodels

TL;DR

This paper introduces a new method for deriving topologies from spaces using elementary submodels, providing insights into Lindelöf spaces and addressing open questions in topology.

Contribution

It defines and explores the properties of the $X/M$ construction, applying it to obtain new results on Lindelöf spaces and related topological questions.

Findings

Established basic properties of the $X/M$ construction.

Analyzed the topological relationship between $X$ and $X/M$.

Provided partial answers to open questions about Lindelöf spaces.

Abstract

This article is an investigation of a method of deriving a topology from a space and an elementary submodel containing it. We first define and give the basic properties of this construction, known as $X/M$. In the next section, we construct some examples and analyse the topological relationship between $X$ and $X/M$. In the final section, we apply $X/M$ to get novel results about Lindel\"{o}f spaces, giving partial answers to a question of F.D. Tall and another question of Tall and M. Scheepers.