Knaster-Kuratowski fan

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In topology, Knaster-Kuratowski fan (also known as the "Cantor leaky tent" or "Cantor teepee") is a connected topological space such that the removal of a single point makes it totally disconnected.

Let C be the Cantor set, p the point \left(\frac{1}{2}, \frac{1}{2}\right) and L(c), for c \in C, denote the line segment connecting c and p. If c \in C is an endpoint of an interval deleted in the Cantor set, let X_{c} = \{ x \in L(c) : x \in Q \}; for all other points let X_{c} = \{ x \in L(c) : x \notin Q \}; the Knaster-Kuratowski fan is defined as \bigcup_{c \in C} X_{c}.

The fan itself is connected, but becomes totally disconnected upon the removal of p = \left(\frac{1}{2}, \frac{1}{2}\right).

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