Knaster-Kuratowski fan

The Knaster-Kuratowski fan provides an example of a connected space, such that the removal of a single point produces a totally disconnected space.

The Knaster-Kuratowski fan has a dispersion point; any space with the particular point topology has an explosion point.

If is an endpoint of an interval deleted in the Cantor set, let ; for all other points in let ; the Knaster-Kuratowski fan is defined as .

In topology, a branch of mathematics, the Knaster-Kuratowski 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.