Lipscomb's \(L(A)\) space fractalized in \(l^p (A)\)

DOI10.1007/s00009-011-0133-9zbMath1253.28004OpenAlexW2067461864MaRDI QIDQ1758631

Alexandru Mihail, Radu Miculescu

Publication date: 15 November 2012

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-011-0133-9

zbMATH Keywords

infinite iterated function systemattractor of an infinite IFSLipscomb's space

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Fractals (28A80) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

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The canonical projection between the shift space of an IIFS and its attractor as a fixed point ⋮ Alternative characterization of hyperbolic affine infinite iterated function systems ⋮ Type \(\mathcal{A}\) sets and the attractors of infinite iterated function systems

Cites Work

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• Lipscomb's L(A) Space Fractalized in Hilbert's l 2 (A) Space
• On Imbedding Finite-Dimensional Metric Spaces
• Lipscomb’s universal space is the attractor of an infinite iterated function system
• Lipscomb's space $\omega^{A}$ is the attractor of an infinite IFS containing affine transformations of $l^{2}(A)$