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 ] . 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 c -algebrable sets. The argument is based on a criterion of strong c -algebrability using compositions with exponential like functions.