Nonseparable spaceability and strong algebrability of sets of continuous singular functions

Let CBV denote the Banach algebra of all continuous real-valued functions of bounded variation, defined in [0,1][0,1]. We show that the set of strongly singular functions in CBV is nonseparably spaceable. We also prove that certain families of singular functions constitute strongly cc-algebrable sets. The argument is based on a criterion of strong cc-algebrability using compositions with exponential like functions.