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1997 | 153 | 2 | 125-40
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A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

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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.
Opis fizyczny
  • Faculty of Mathematics and Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
  • Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
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