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