We investigate properties of strongly useful topologies, i.e., topologies with respect to which every weakly continuous preorder admits a continuous order-preserving function. In particular, we prove that a topology is strongly useful provided that the topology generated by every family of separable systems is countable. Focusing on normal Hausdorff topologies, whose consideration is fully justified and not restrictive at all, we show that strongly useful topologies are hereditarily separable on closed sets, and we identify a simple condition under which the Lindelöf property holds.

Properties of Topologies for the Continuous Representability of All Weakly Continuous Preorders

Gianni Bosi;Laura Franzoi;Gabriele Sbaiz
2023-01-01

Abstract

We investigate properties of strongly useful topologies, i.e., topologies with respect to which every weakly continuous preorder admits a continuous order-preserving function. In particular, we prove that a topology is strongly useful provided that the topology generated by every family of separable systems is countable. Focusing on normal Hausdorff topologies, whose consideration is fully justified and not restrictive at all, we show that strongly useful topologies are hereditarily separable on closed sets, and we identify a simple condition under which the Lindelöf property holds.
2023
18-ott-2023
Pubblicato
https://www.mdpi.com/2227-7390/11/20/4335
File in questo prodotto:
File Dimensione Formato  
BosiFranzoiSbaiz_mathematics-11-04335.pdf

accesso aperto

Descrizione: articolo
Tipologia: Documento in Versione Editoriale
Licenza: Creative commons
Dimensione 277.42 kB
Formato Adobe PDF
277.42 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/11368/3061018
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact