# Sierpiński curve

From Encyclopedia of Mathematics

*Sierpiński carpet*

An example of a Cantor curve that contains a subset homeomorphic to any given Cantor curve. It was constructed by W. Sierpiński ; for its construction see Line (curve). This curve has at each point continual branching index.

#### References

[1a] | W. Sierpiński, "Sur une courbe dont tout point est un point de ramification" C.R. Acad. Sci. Paris , 160 (1915) pp. 302–305 |

[1b] | W. Sierpiński, "Sur une courbe cantorienne qui contient une image binniro que et continue de toute courbe donnée" C.R. Acad. Sci. Paris , 162 (1916) pp. 629–632 |

[2] | P.S. Aleksandrov, "Einführung in die Mengenlehre und die allgemeine Topologie" , Deutsch. Verlag Wissenschaft. (1984) (Translated from Russian) |

[3] | K. Kuratowski, "Topology" , 2 , Acad. Press (1968) (Translated from French) |

**How to Cite This Entry:**

Sierpiński curve.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Sierpi%C5%84ski_curve&oldid=13908

This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article