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


Author: Witold Marciszewski
Journal: Proc. Amer. Math. Soc. 126 (1998), 319-321
MSC (1991): Primary 57N17
DOI: https://doi.org/10.1090/S0002-9939-98-04393-7
MathSciNet review: 1452812
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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.


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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: https://doi.org/10.1090/S0002-9939-98-04393-7
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
Article copyright: © Copyright 1998 American Mathematical Society