We introduce an upper semicontinuity condition concerning a not necessarily total preorder on a topological space, namely strong upper semicontinuity, and in this way we extend to the nontotal case the famous Rader’s theorem,which guarantees the existence of an upper semicontinuous order-preserving function for an upper semicontinuous total preorder on a second countable topological space. We show that Rader’s theorem is not generalizable if we adopt weaker upper semicontinuity conditions already introduced in the literature. We characterize the existence of an upper semicontinuous order-preserving function for all strongly upper semicontinuous preorders on a metrizable topological space.

A simple characterization of the existence of upper semicontinuous order-preserving functions

Gianni Bosi
;
Laura Franzoi
2023-01-01

Abstract

We introduce an upper semicontinuity condition concerning a not necessarily total preorder on a topological space, namely strong upper semicontinuity, and in this way we extend to the nontotal case the famous Rader’s theorem,which guarantees the existence of an upper semicontinuous order-preserving function for an upper semicontinuous total preorder on a second countable topological space. We show that Rader’s theorem is not generalizable if we adopt weaker upper semicontinuity conditions already introduced in the literature. We characterize the existence of an upper semicontinuous order-preserving function for all strongly upper semicontinuous preorders on a metrizable topological space.
2023
18-giu-2023
Pubblicato
https://link.springer.com/article/10.1007/s40505-023-00251-9
File in questo prodotto:
File Dimensione Formato  
BosiFranzoiETBU2023.pdf

accesso aperto

Descrizione: articolo
Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 225.58 kB
Formato Adobe PDF
225.58 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/3059258
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact