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Portal:Alexander horned sphere
[[Image:Alexander horned sphere.png|thumb|300px|right|Alexander horned sphere]]

The '''Alexander horned sphere''' is one of the most famous [[pathological (mathematics)|pathological example]]s in [[mathematics]], discovered  by {{harvs|txt|authorlink=James Waddell Alexander II|first=J. W. |last=Alexander|year=1924}}. It is the particular [[embedding (topology)|embedding]] of a [[sphere]] in 3-dimensional [[Euclidean space]] obtained by the following construction, starting with(contracted; show full)

Other substantially different constructions exist for constructing such "wild" spheres. Another famous example, also from Alexander, is [[Antoine's horned sphere]], which is based on [[Antoine's necklace]], a pathological embedding of the [[Cantor set]] into the 3-sphere.

==See also==
⏎
⏎
*[[Cantor tree surface]]
*[[Fox–Artin arc]]

==References==
* {{Citation | last1=Alexander | first1=J. W. | author1-link=James Waddell Alexander II | title=An Example of a Simply Connected Surface Bounding a Region which is not Simply Connected | url=http://www.jstor.org/stable/84202 | publisher=National Academy of Sciences | year=1924 | journal=[[Proceedings of the National Academy of Sciences|Proceedings of the National Academy of Sciences of the United States of America]] | issn=0027-8424 | volume=10 | issue=1 | pages= 8–10}}
(contracted; show full)
[[ca:Esfera banyada d'Alexander]]
[[es:Esfera cornuda de Alexander]]
[[fr:Sphère cornue d'Alexander]]
[[ko:알렉산더의 뿔 달린 구]]
[[it:Sfera di Alexander]]
[[pl:Rogata sfera Alexandera]]
[[ru:Дикая сфера]]