Sierpiński curve

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)