and Applied Analysis 3 Then, as L[a, b] ⊂ HK([a, b]) it holds that dim(L[a, b]) ≤ dim(HK([a, b])) ≤ card(HK([a, b])). Therefore, by Lemma 8, Corollary 7 and the known fact that c0 = c, we obtain the desired conclusion. Hereafter, the Alexiewicz topology and the topology induced by the norm of Proposition 9 will be denoted as τ A and τ ‖⋅‖ , respectively. Proposition 10. The topology τ ‖⋅‖ on HK...
