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

Marciszewski, Witold

Fundamenta Mathematicae, Tome 154 (1997), p. 125-40 / Harvested from The Polish Digital Mathematics Library

Résumé

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) $\times ℝ$ . One of these examples is compact. This answers some questions of Arkhangel’skiĭ.

Publié le : 1997-01-01

Zbl 0904.46017

EUDML-ID : urn:eudml:doc:212217

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     author = {Witold Marciszewski},
     title = {A function space Cp(X) not linearly homeomorphic to Cp(X) $\times$ $\mathbb{R}$},
     journal = {Fundamenta Mathematicae},
     volume = {154},
     year = {1997},
     pages = {125-40},
     zbl = {0904.46017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv153i2p125bwm}
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Marciszewski, Witold. A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ. Fundamenta Mathematicae, Tome 154 (1997) pp. 125-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv153i2p125bwm/

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