Order and uo-convergence in spaces of continuous functions

2021/10/17 by Bilokopytov, Eugene, Troitsky, Vladimir G.
#06E99 #46A40 #46E25 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.2110.08709

Abstract

We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions C(Ω), C_b(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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