Geodesic
A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ
Fundamenta Mathematicae, Tome 153 (1997) no. 2, pp. 125-40 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We construct two examples of infinite spaces $X$ such that there is no continuous linear surjection from the space of continuous functions $c_p(X)$ onto $c_p(X) × ℝ$. In particular, $c_p(X)$ is not linearly homeomorphic to $c_p(X) × ℝ$. One of these examples is compact. This answers some questions of Arkhangel'skiĭ.
DOI : 10.4064/fm-153-2-125-40
Keywords: function space, pointwise convergence topology, $c_p(X)$, linear homeomorphism

Witold Marciszewski 1

1 
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     title = {A function space {Cp(X)} not linearly homeomorphic to {Cp(X)} {\texttimes} {\ensuremath{\mathbb{R}}}},
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Witold  Marciszewski. A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ. Fundamenta Mathematicae, Tome 153 (1997) no. 2, pp. 125-40. doi: 10.4064/fm-153-2-125-40

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