Order and uoconvergence in spaces of continuous functions
Abstract
We present several characterizations of uoconvergent 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 uoconverges iff it converges pointwise on a comeagre set. We also characterize order bounded sets in spaces of continuous functions. This leads to characterizations of order convergence.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08709
 Bibcode:
 2021arXiv211008709B
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  General Topology;
 46A40;
 46E25;
 06E99
 EPrint:
 13 pages