Cantor tree surface

An Alexander horned sphere. Its non-singular points form a Cantor tree surface.

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.

See also

• Jacob's ladder surface
• Loch Ness monster surface

References

• Ghys, Étienne (1995), "Topologie des feuilles génériques", Annals of Mathematics, Second Series 141 (2): 387–422, doi:10.2307/2118526, ISSN 0003-486X 
• 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)], 64, Birkhäuser Verlag, ISBN 978-3-7643-7091-6, https://books.google.com/books?id=Tl4WkcHzhIAC