• Corpus ID: 239016540

Order and uo-convergence in spaces of continuous functions

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