Abstract
We prove the existence of three subspaces of $C[0,1]$, each homeomorphic to $C[0,1]$; the first consists only of infinitely many times differentiable functions, the second consists only of singular functions of bounded variation, and the third consists only of nowhere differentiable functions.
Citation
F. S. Cater. "On sparse subspaces of C[0,1].." Real Anal. Exchange 31 (1) 7 - 12, 2005-2006.
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