Difference between revisions 107880290 and 107880291 on dewiki

[[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]]a wild embedding of a sphere into space, 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 a [[standard torus]]:
#Remove a radial slice of the torus.
#Connect a standard punctured torus to each side of the cut, interlinked with the torus on the other side.
(contracted; show full)

One can generalize Alexander's construction to generate other horned spheres by increasing the number of horns at each stage of Alexander's construction or considering the analogous construction in higher dimensions.  

Other substantially different constructions exist for constructing such "wild" spheres. Another 
famous example, also fromound by 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==
(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]]