Nonseparable spaceability and strong algebrability of sets of continuous singular functions

By M. Balcerzak, A. Bartoszewicz, M. Filipczak. 2013

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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 new general criterion of strong c-algebrability.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/674667a1e6c77299e581dfcb585f1e9c583292a6