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Cantor tree surface

Infinite-genus surface homeomorphic to a sphere with a Cantor set removed

In dynamical systems, the Cantor tree is an infinite-genus surface homeomorphic to a sphere with a Cantor set removed. The blooming Cantor tree is a Cantor tree with an infinite number of handles added in such a way that every end is a limit of handles.

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References

Ghys, Étienne (1995), "Topologie des feuilles génériques", Annals of Mathematics, Second Series (in French), 141 (2): 387–422, doi:10.2307/2118526, ISSN 0003-486X, JSTOR 2118526, MR 1324140 /wiki/Annals_of_Mathematics ↩
Walczak, Paweł (2004), Dynamics of foliations, groups and pseudogroups, Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series) [Mathematics Institute of the Polish Academy of Sciences. Mathematical Monographs (New Series)], vol. 64, Birkhäuser Verlag, p. 210, ISBN 978-3-7643-7091-6, MR 2056374 978-3-7643-7091-6 ↩

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