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On the Orderability Problem and the Interval Topology

In: Topics in Mathematical Analysis and Applications

Author

Listed:
  • Kyriakos Papadopoulos

    (Engineering, American University of the Middle East)

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.

Suggested Citation

  • Kyriakos Papadopoulos, 2014. "On the Orderability Problem and the Interval Topology," Springer Optimization and Its Applications, in: Themistocles M. Rassias & László Tóth (ed.), Topics in Mathematical Analysis and Applications, edition 127, pages 601-608, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-06554-0_27
    DOI: 10.1007/978-3-319-06554-0_27
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