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On van Mill's example of a normed $X$ with $X\not \approx X\times \mathbb{R}$

Author(s): Witold Marciszewski
Journal: Proc. Amer. Math. Soc. 126 (1998), 319-321.
MSC (1991): Primary 57N17
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Abstract: In 1987 van Mill constructed an infinite-dimensional normed space $X$ which is not homeomorphic with the product $X\times \mathbb{R}$ . We give a short proof of this property of van Mill's example.

References:

[Ke]: A. S. Kechris, Classical Descriptive Set Theory, Springer-Verlag, New York, 1995. MR 96e:03057
[Ku]: K. Kuratowski, Applications of the Baire-category method to the problem of independent sets, Fund. Math. 81 (1973), 65-72. MR 49:3855
[vM]: J. van Mill, Domain invariance in infinite-dimensional linear spaces, Proc. Amer. Math. Soc. 101 (1987), 173-180. MR 88k:57023
[My]: J. Mycielski, Almost every function is independent, Fund. Math. 81 (1973), 43-48. MR 49:3854

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Additional Information:

Witold Marciszewski
Affiliation: Vrije Universiteit, Faculty of Mathematics and Computer Science, De Boelelaan 1081 a, 1081 HV Amsterdam, The Netherlands
Address at time of publication: Institute of Mathematics, University of Warsaw, Banacha 2, 02--097 War- szawa, Poland
Email: wmarcisz@mimuw.edu.pl

DOI: 10.1090/S0002-9939-98-04393-7
PII: S 0002-9939(98)04393-7
Keywords: Metric linear space, normed space
Received by editor(s): September 9, 1996
Received by editor(s) in revised form: March 14, 1997
Additional Notes: Research partially supported by KBN grant 2 P301 024 07.
Communicated by: Alan Dow
Copyright of article: Copyright 1998, American Mathematical Society

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The following works have cited this article

N\'u\tilde nez Garc\'\i a, Juana, Refining two Marciszewski's constructions related to the Sierpi\'nski-Kuratowski technique, Bull. Polish Acad. Sci. Math. 47 (1999), 157--161. (English) MR 2000e:57036


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