Nests, and their Role in the Orderability Problem
Kyriakos Papadopoulos
TL;DR
This paper surveys recent developments on nests and the orderability problem, and presents new results, partial findings, and open questions related to nests in various ordered structures and spaces.
Contribution
It provides a comprehensive overview of nests in order theory and introduces new insights and open questions in the context of connected LOTS, product spaces, and the Fermat Real Line.
Findings
Survey of recent results on nests and orderability
New partial results and open questions in the field
Application to connected LOTS and Fermat Real Line
Abstract
This chapter is divided into two parts. The first part is a survey of some recent results on nests and the orderability problem. The second part consists of results, partial results and open questions, all viewed in the light of nests. From connected LOTS, to products of LOTS and function spaces, up to an order relation in the Fermat Real Line.
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