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Order and uo-convergence in spaces of continuous functions

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Eugene Bilokopytov, Vladimir G. Troitsky

Functional Analysis · Submitted 17 Oct 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, it is shown that a sequence uo-converges iff it converges pointwise on a co-meagre set.

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arXiv ID2110.08709 (version 1)
Pith IDXFOEWYLR, Pith's permanent record of this paper and its review
CitationEugene Bilokopytov, Vladimir G. Troitsky. "Order and uo-convergence in spaces of continuous functions." arXiv:2110.08709 (2021). https://pith.science/paper/XFOEWYLR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,567 input tokens.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. 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.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. contribution 1.00 0.93 0.28 asserted 1.00
s1 In particular, it is shown that a sequence uo-converges iff it converges pointwise on a co-meagre set. result 1.00 0.93 0.54 asserted 1.00
s2 We also characterize order bounded sets in spaces of continuous functions. contribution 0.65 0.94 0.10 asserted 0.99
s3 This leads to characterizations of order convergence. result 0.80 0.91 0.13 asserted 0.98

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. 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.

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