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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lipscomb’s space $\omega ^{A}$ is the attractor of an infinite IFS containing affine transformations of $l^{2}(A)$
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by Radu Miculescu and Alexandru Mihail PDF
Proc. Amer. Math. Soc. 136 (2008), 587-592 Request permission

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.
References
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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
  • 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
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 587-592
  • MSC (2000): Primary 37C70; Secondary 54H05, 54B15
  • DOI: https://doi.org/10.1090/S0002-9939-07-08981-2
  • MathSciNet review: 2358499