Namespaces
Variants
Actions

Sierpiński curve

From Encyclopedia of Mathematics
Jump to: navigation, search
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

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=23526
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article