Open Access
2008/2009 Multiplying Balls in Cⁿ[0,1]
Artur Wachowicz
Real Anal. Exchange 34(2): 445-450 (2008/2009).


Let $C^{(n)}[0,1]$ stand for the Banach space of functions $f:[0,1]\rightarrow \mathbb{R}$ with continuous $n$ -th derivative. We prove that if $B_{1},B_{2}$ are open balls in $C^{(n)}[0,1]$ then the set $B_{1}\cdot B_{2}=\{f\cdot g:f\in B_{1},g\in B_{2}\}$ has non-empty interior in $C^{(n)}[0,1].$ This extends the result of [1] dealing with the space of continuous functions on $[0,1]$.


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Artur Wachowicz. "Multiplying Balls in Cⁿ[0,1]." Real Anal. Exchange 34 (2) 445 - 450, 2008/2009.


Published: 2008/2009
First available in Project Euclid: 29 October 2009

zbMATH: 1184.46051
MathSciNet: MR2569197

Primary: 46B25 , 46J10
Secondary: 26A15

Keywords: Baire category , multiplication , Residual set

Rights: Copyright © 2008 Michigan State University Press

Vol.34 • No. 2 • 2008/2009
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