let formula_1 be the cantor set, let formula_2 be the point formula_3, and let formula_4, for formula_5, denote the line segment connecting formula_6 to formula_2. if formula_5 is an endpoint of an interval deleted in the cantor set, let formula_9; for all other points in formula_1 let formula_11; the knaster–kuratowski fan is defined as formula_12 equipped with the subspace topology inherited from the standard topology on formula_13.