Sierpiński curve

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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.


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