Order and uo-convergence in spaces of continuous functions

Order and uo-convergence in spaces of continuous functions

We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions C(Ω), Cb(Ω), C0(Ω), and C∞(Ω), extending results of [11]. In particular, it is shown that a sequence uo-converges iff it converges pointwise on a co-meagre set. We also characterize order bounde...

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Veröffentlicht in:Topology and its applications 2022-03, Vol.308, p.107999, Article 107999
Hauptverfasser: Bilokopytov, Eugene, Troitsky, Vladimir G.
Format: Artikel
Sprache:eng
Schlagworte:
Banach lattice
Continuous functions
Order convergence
Vector lattice
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Zusammenfassung:We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions C(Ω), Cb(Ω), C0(Ω), and C∞(Ω), extending results of [11]. In particular, it is shown that a sequence uo-converges iff it converges pointwise on a co-meagre set. We also characterize order bounded sets in spaces of continuous functions. This leads to characterizations of order convergence.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2022.107999