Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions

Authors

  • Gianni Bosi Università di Trieste
  • Romano Isler Università di Trieste

DOI:

https://doi.org/10.4995/agt.2000.3026

Keywords:

Topological preordered space, Decreasing scale, Order-preserving function

Abstract

We characterize the existence of a real continuous order-preserving function on a topological preordered space, under the hypotheses that the topological space is normal and the preorder satisfies a strong continuity assumption, called IC-continuity. Under the same continuity assumption concerning the preorder, we present a sufficient condition for the existence of a continuous order-preserving function in case that the topological space is completely regular.

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Author Biographies

Gianni Bosi, Università di Trieste

Dipartimento di Matematica Applicata

Romano Isler, Università di Trieste

Dipartimento di Matematica Applicata

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Published

2000-10-01

How to Cite

[1]
G. Bosi and R. Isler, “Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions”, Appl. Gen. Topol., vol. 1, no. 1, pp. 93–98, Oct. 2000.

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Articles