Knaster–Kuratowski fan

In topology, a branch of mathematics, the Knaster–Kuratowski fan (named after Polish mathematicians Bronisław Knaster and Kazimierz Kuratowski) is a specific connected topological space with the property that the removal of a single point makes it totally disconnected.

It is also known as Cantor's leaky tent or Cantor's teepee (after Georg Cantor), depending on the presence or absence of the apex.

be the Cantor set, let

be the point

, denote the line segment connecting

is an endpoint of an interval deleted in the Cantor set, let

; for all other points in

; the Knaster–Kuratowski fan is defined as

equipped with the subspace topology inherited from the standard topology on

The fan itself is connected, but becomes totally disconnected upon the removal of

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