Order and uo-convergence in spaces of continuous functions

Eugene Bilokopytov; Vladimir G. Troitsky

Order and uo-convergence in spaces of continuous functions

Functional Analysis 2021-10-19 v1 General Topology

Authors: Eugene Bilokopytov , Vladimir G. Troitsky

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.

Keywords

uo-convergence order convergence spaces of continuous functions co-meagre set order bounded sets pointwise convergence

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@article{arxiv.2110.08709,
  title  = {Order and uo-convergence in spaces of continuous functions},
  author = {Eugene Bilokopytov and Vladimir G. Troitsky},
  journal= {arXiv preprint arXiv:2110.08709},
  year   = {2021}
}

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13 pages

Order and uo-convergence in spaces of continuous functions

Abstract

Keywords

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