On the Orderability Problem and the Interval Topology

Kyriakos Papadopoulos ()
Additional contact information
Kyriakos Papadopoulos: Engineering, American University of the Middle East

A chapter in Topics in Mathematical Analysis and Applications, 2014, pp 601-608 from Springer

Abstract: Abstract The class of LOTS (linearly ordered topological spaces, i.e. spaces equipped with a topology generated by a linear order) 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. The Orderability Problem, a very important question on whether a topological space admits a linear order which generates a topology equal to the topology of the space, was given a general solution by van Dalen and Wattel (Gen. Topol. Appl. 3:347–354, 1973). In this article we first examine the role of the interval topology in van Dalen’s and Wattel’s characterization of LOTS, and we then discuss ways to extend this model to transitive relations that are not necessarily linear orders.

Keywords: Orderability problem; Nest; LOTS; Interval topology (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-06554-0_27

Ordering information: This item can be ordered from
http://www.springer.com/9783319065540

DOI: 10.1007/978-3-319-06554-0_27

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().