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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lipscomb's space $ \omega^{A}$ is the attractor of an infinite IFS containing affine transformations of $ l^{2}(A)$


Authors: Radu Miculescu and Alexandru Mihail
Journal: Proc. Amer. Math. Soc. 136 (2008), 587-592
MSC (2000): Primary 37C70; Secondary 54H05, 54B15
Published electronically: November 2, 2007
MathSciNet review: 2358499
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Abstract: It is known that Lipscomb's space $ L(A)$ can be imbedded in Hilbert's space $ l^{2}(A)$. Let $ \omega ^{A}$ be the imbedded version of $ L(A)$ endowed with the $ l^{2}(A)$-induced topology. We show how to construct $ \omega ^{A}$ as the attractor of an iterated function system containing an infinite number of affine transformations of $ l^{2}(A)$. In this way we answer an open question of J.C. Perry.


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Additional Information

Radu Miculescu
Affiliation: Department of Mathematics, Bucharest University, Bucharest, Academiei Street 14, Romania
Email: miculesc@yahoo.com

Alexandru Mihail
Affiliation: Department of Mathematics, Bucharest University, Bucharest, Academiei Street 14, Romania
Email: mihailalex68@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08981-2
PII: S 0002-9939(07)08981-2
Keywords: Lipscomb's space, infinite iterated function system
Received by editor(s): May 29, 2006
Received by editor(s) in revised form: October 1, 2006, and October 26, 2006
Published electronically: November 2, 2007
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.