A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

• Autorzy: Witold Marciszewski
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

function space; pointwise convergence topology; $c_p(X)$; linear homeomorphism

Kategorie tematyczne

• 54C35: Function spaces
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 153
• Numer: 2
• Strony: 125-40

Daty

wydano

1997

otrzymano

1996-06-01

poprawiono

1997-03-03

Twórcy

autor

Witold Marciszewski

• 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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