Ferrando and Lüdkovsky proved that for a non-empty set Ω normed space X, the c0(Ω,X) is barrelled, ultrabornological, or unordered Baire-like if only X is, respectively, Baire-like. When metrizable locally convex space, with an increasing sequence of semi-norms .n∈N defining its topology, then over field K (of real complex numbers) all functions f:Ω→X such each ε>0 n∈N ω∈Ω:f(ω)n>ε finite ...
