Portal de Periódicos da CAPES

Continuous representability of semiorders

2007; Elsevier BV; Volume: 52; Issue: 1 Linguagem: Inglês

10.1016/j.jmp.2007.09.006

1096-0880

María Jesús Campión, Juan C. Candeal, Esteban Induráin, Margarita Zudaire,

Advanced Topology and Set Theory

In the framework of the analysis of orderings whose associated indifference relation is not transitive, we study the structure of a semiorder, paying attention to the problem of its continuous representability through a real-valued function and a positive threshold. For the case of connected topological spaces, we obtain a full characterization of the continuous representability of semiorders without extremal elements.