Zerner, Martin P. W. Weak separation properties for self-similar sets. (English) Zbl 0874.54025 Proc. Am. Math. Soc. 124, No. 11, 3529-3539 (1996). Summary: We develop a theory for self-similar sets in \(\mathbb{R}^s\) that fulfill the weak separation property of Lau and Ngai, which is weaker than the open set condition of Hutchinson. Cited in 66 Documents MSC: 54E40 Special maps on metric spaces 54H15 Transformation groups and semigroups (topological aspects) 28A78 Hausdorff and packing measures Keywords:fractals; self-similar sets; weak separation property × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Robert B. Ash, Real analysis and probability, Academic Press, New York-London, 1972. Probability and Mathematical Statistics, No. 11. · Zbl 0249.28001 [2] Christoph Bandt and Siegfried Graf, Self-similar sets. VII. A characterization of self-similar fractals with positive Hausdorff measure, Proc. Amer. Math. Soc. 114 (1992), no. 4, 995 – 1001. · Zbl 0823.28003 [3] K. J. Falconer, Dimensions and measures of quasi self-similar sets, Proc. Amer. Math. Soc. 106 (1989), no. 2, 543 – 554. · Zbl 0683.58034 [4] Kenneth Falconer, Fractal geometry, John Wiley & Sons, Ltd., Chichester, 1990. Mathematical foundations and applications. · Zbl 0689.28003 [5] Michael Klemm, Symmetrien von Ornamenten und Kristallen, Springer-Verlag, Berlin-New York, 1982 (German). Hochschultext. · Zbl 0482.20034 [6] K.-S. Lau and S.-M. Ngai, Multifractal measures and a weak separation condition, Adv. Math. (to appear). · Zbl 0929.28007 [7] J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1 – 7. · Zbl 0162.25401 [8] Andreas Schief, Separation properties for self-similar sets, Proc. Amer. Math. Soc. 122 (1994), no. 1, 111 – 115. · Zbl 0807.28005 [9] N. Smythe, Growth functions and Euler series, Invent. Math. 77 (1984), no. 3, 517 – 531. · Zbl 0577.20020 · doi:10.1007/BF01388836 [10] Philip Wagreich, The growth function of a discrete group, Group actions and vector fields (Vancouver, B.C., 1981) Lecture Notes in Math., vol. 956, Springer, Berlin, 1982, pp. 125 – 144. · doi:10.1007/BFb0101514 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.