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| Alexander horned sphere ： ウィキペディア英語版 |
Alexander horned sphere
The Alexander horned sphere is a pathological object in topology discovered by .
==Construction==
The Alexander horned sphere is the particular 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.
#Repeat steps 1–2 on the two tori just added ''ad infinitum''.
By considering only the points of the tori that are not removed at some stage, an embedding results of the sphere with a Cantor set removed. This embedding extends to the whole sphere, since points approaching two different points of the Cantor set will be at least a fixed distance apart in the construction.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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