### Abstract

Under some conditions concerning the weak contractions f_{j} (d(f_{j}(x), f_{j}(y)) ≦ α_{j}(l)d(x, y) for d(x, y) < l, l > 0, 0 < α_{j}(l) < 1), j = 1, ..., m defined on a compact metric space X, a decomposition space of the weak self-similar set generated by the system f_{j}, j = 1, ..., m is proved to be homeomorphic to X.

Original language | English |
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Pages (from-to) | 785-787 |

Number of pages | 3 |

Journal | Chaos, Solitons and Fractals |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 May |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics

### Cite this

*Chaos, Solitons and Fractals*,

*24*(3), 785-787. https://doi.org/10.1016/j.chaos.2004.09.083

**On a decomposition space of a weak self-similar set.** / Kitada, Akihiko; Ogasawara, Yoshihito.

Research output: Contribution to journal › Article

*Chaos, Solitons and Fractals*, vol. 24, no. 3, pp. 785-787. https://doi.org/10.1016/j.chaos.2004.09.083

}

TY - JOUR

T1 - On a decomposition space of a weak self-similar set

AU - Kitada, Akihiko

AU - Ogasawara, Yoshihito

PY - 2005/5

Y1 - 2005/5

N2 - Under some conditions concerning the weak contractions fj (d(fj(x), fj(y)) ≦ αj(l)d(x, y) for d(x, y) < l, l > 0, 0 < αj(l) < 1), j = 1, ..., m defined on a compact metric space X, a decomposition space of the weak self-similar set generated by the system fj, j = 1, ..., m is proved to be homeomorphic to X.

AB - Under some conditions concerning the weak contractions fj (d(fj(x), fj(y)) ≦ αj(l)d(x, y) for d(x, y) < l, l > 0, 0 < αj(l) < 1), j = 1, ..., m defined on a compact metric space X, a decomposition space of the weak self-similar set generated by the system fj, j = 1, ..., m is proved to be homeomorphic to X.

UR - http://www.scopus.com/inward/record.url?scp=12244278301&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12244278301&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2004.09.083

DO - 10.1016/j.chaos.2004.09.083

M3 - Article

VL - 24

SP - 785

EP - 787

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 3

ER -