Nonlinear disjointness/supplement preservers of nonnegative continuous functions

Lei Li, Ching Jou Liao, Luoyi Shi, Liguang Wang, Ngai Ching Wong*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


Let F(X),F(Y) be sufficiently large sets of nonnegative continuous real-valued functions defined on completely regular spaces X,Y, respectively. Let Φ:F(X)→F(Y) be a surjective map satisfying that f∨g>0⟺Φ(f)∨Φ(g)>0,∀f,g∈F(X). In many cases, we show that there is a homeomorphism τ:Y→X such that Φ(f)(y)≠0⟺f(τ(y))≠0,∀f∈F(X),∀y∈Y. Assume X,Y are locally compact Hausdorff (resp. separable and metrizable) and Φ:C0(X)+→C0(Y)+ (resp. Φ:Cb(X)+→Cb(Y)+) is a surjective map. We show that Φ preserves the norms of infima, i.e., ‖Φ(f)∧Φ(g)‖=‖f∧g‖,∀f,g∈C0(X)+ (resp.Cb(X)+), if and only if there is a homeomorphism τ:Y→X such that Φ(f)(y)=f(τ(y)),∀f∈C0(X)+ (resp.Cb(X)+), ∀y∈Y.

Original languageEnglish
Article number127483
JournalJournal of Mathematical Analysis and Applications
Issue number1
Early online date7 Jun 2023
Publication statusPublished - 1 Dec 2023

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Continuous functions
  • Cozero sets
  • Disjointness preservers
  • Kaplansky theorem
  • Order isomorphism


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