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

Gianni Bosi, Romano Isler


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.


Topological preordered space; Decreasing scale; Order-preserving function

Subject classification

06A06; 54F30

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1. Continuous multi-utility representations of preorders
Gianni Bosi, Gerhard Herden
Journal of Mathematical Economics  vol: 48  issue: 4  first page: 212  year: 2012  
doi: 10.1016/j.jmateco.2012.05.001

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147