# Order and uo-convergence in spaces of continuous functions

@inproceedings{Bilokopytov2021OrderAU, title={Order and uo-convergence in spaces of continuous functions}, author={Eugene Bilokopytov and Vladimir G. Troitsky}, year={2021} }

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 [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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