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

Witold Marciszewski

Fundamenta Mathematicae (1997)

  • Volume: 153, Issue: 2, page 125-40
  • ISSN: 0016-2736

Abstract

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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 . I n p a r t i c u l a r , cp(X) i s n o t l i n e a r l y h o m e o m o r p h i c t o cp(X) × ℝ . One of these examples is compact. This answers some questions of Arkhangel’skiĭ.

How to cite

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Marciszewski, Witold. "A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ." Fundamenta Mathematicae 153.2 (1997): 125-40. <http://eudml.org/doc/212217>.

@article{Marciszewski1997,
abstract = {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, $cp(X)$ is not linearly homeomorphic to $cp(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel’skiĭ.},
author = {Marciszewski, Witold},
journal = {Fundamenta Mathematicae},
keywords = {function space; pointwise convergence topology; $c_p(X)$; linear homeomorphism; continuous linear surjection},
language = {eng},
number = {2},
pages = {125-40},
title = {A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ},
url = {http://eudml.org/doc/212217},
volume = {153},
year = {1997},
}

TY - JOUR
AU - Marciszewski, Witold
TI - A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ
JO - Fundamenta Mathematicae
PY - 1997
VL - 153
IS - 2
SP - 125
EP - 40
AB - 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, $cp(X)$ is not linearly homeomorphic to $cp(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel’skiĭ.
LA - eng
KW - function space; pointwise convergence topology; $c_p(X)$; linear homeomorphism; continuous linear surjection
UR - http://eudml.org/doc/212217
ER -

References

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