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arXiv · 1301.5162

Nonseparable spaceability and strong algebrability of sets of continuous singular functions

Marek Balcerzak·Artur Bartoszewicz·Malgorzata Filipczak
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Abstract

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.

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Marek Balcerzak, Artur Bartoszewicz, Malgorzata Filipczak. 2013-01-22. Nonseparable spaceability and strong algebrability of sets of continuous singular functions. https://arxiv.org/abs/1301.5162

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