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Knaster–Kuratowski fan
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Knaster–Kuratowski fan : ウィキペディア英語版
Knaster–Kuratowski fan

In topology, a branch of mathematics, the KnasterKuratowski fan (also known as Cantor's leaky tent or Cantor's teepee depending on the presence or absence of the apex) is a connected topological space with the property that the removal of a single point makes it totally disconnected.
Let C be the Cantor set, let p be the point (\tfrac, \tfrac)\in\mathbb R^2, and let L(c), for c \in C, denote the line segment connecting (c,0) to p. If c \in C is an endpoint of an interval deleted in the Cantor set, let X_ = \; for all other points in C let X_ = \; the Knaster–Kuratowski fan is defined as \bigcup_ X_ equipped with the subspace topology inherited from the standard topology on \mathbb^2.
The fan itself is connected, but becomes totally disconnected upon the removal of p.
==References==

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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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