Semigroups satisfying P-condition and topological self-similar sets
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 461-464
Cet article a éte moissonné depuis la source Math-Net.Ru
We give a definition of self-similar sets, which works in Hausdorff topological spaces and prove topological version of Hutchinson theorem without the assumption of completeness of the space.
Keywords:
self-similar sets, self-similar structure, Hausdorff topological space.
Mots-clés : fractal
Mots-clés : fractal
@article{SEMR_2010_7_a37,
author = {A. V. Tetenov},
title = {Semigroups satisfying {P-condition} and topological self-similar sets},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {461--464},
year = {2010},
volume = {7},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SEMR_2010_7_a37/}
}
A. V. Tetenov. Semigroups satisfying P-condition and topological self-similar sets. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 7 (2010), pp. 461-464. http://geodesic.mathdoc.fr/item/SEMR_2010_7_a37/
[1] W. J. Charatonik and A. Dilks, “On self-homeomorphic spaces”, Topology Appl., 55 (1994), 215–238 | DOI | MR | Zbl
[2] L. Bartholdi, R. I. Grigorchuk, V. V. Nekrashevych, From fractal groups to fractal sets, 2002, arXiv: math.GR/0202001
[3] J. Hutchinson, “Fractals and self-similarity”, Indiana Univ. Math. J., 30:5 (1981), 713–747 | DOI | MR | Zbl
[4] A. Kameyama, “Self-Similar Sets from the Topological Point of View”, Japan J. Indust. Appl. Math., 10 (1993), 85–95 | DOI | MR | Zbl
[5] J. Kigami, “Harmonic calculus on p.c.f, self-similar sets”, Trans. Am. Math. Soc., 335:2 (1993), 721–755 | DOI | MR | Zbl
[6] J. Kigami, Analysis on fractals, Cambridge Tracts in Mathematics, 143, Cambridge University Press, 2001 | MR | Zbl