## Real Analysis Exchange

### On sparse subspaces of C[0,1].

F. S. Cater

#### 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.

#### Article information

Source
Real Anal. Exchange, Volume 31, Number 1 (2005), 7-12.

Dates
First available in Project Euclid: 5 June 2006

https://projecteuclid.org/euclid.rae/1149516800

Mathematical Reviews number (MathSciNet)
MR2218184

Zentralblatt MATH identifier
1104.26007

#### Citation

Cater, F. S. On sparse subspaces of C[0,1]. Real Anal. Exchange 31 (2005), no. 1, 7--12. https://projecteuclid.org/euclid.rae/1149516800

#### References

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