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2005-2006 On sparse subspaces of C[0,1].
F. S. Cater
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Real Anal. Exchange 31(1): 7-12 (2005-2006).


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.


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F. S. Cater. "On sparse subspaces of C[0,1].." Real Anal. Exchange 31 (1) 7 - 12, 2005-2006.


Published: 2005-2006
First available in Project Euclid: 5 June 2006

zbMATH: 1104.26007
MathSciNet: MR2218184

Primary: 26A24 , 26A27 , 26A30 , 54C05

Keywords: differentiable functions , homeomorphism , singular functions.

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 1 • 2005-2006
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