Order and uo-convergence in spaces of continuous functions
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2021
- DOI:
- 10.48550/arXiv.2110.08709
- arXiv:
- arXiv:2110.08709
- Bibcode:
- 2021arXiv211008709B
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - General Topology;
- 46A40;
- 46E25;
- 06E99
- E-Print:
- 13 pages