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We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is homeomorphic to the separable Hilbert space. This result is a special case of a general theorem we prove about spaces of upper semicontinuous functions on compact metric spaces that are strongly discontinuous. © 2010 The Mathematical Society of Japan

The space of Lelek fans in the Cantor fan is homeomorphic to Hilbert space